1.
Carpentry
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Carpentry in the United States is almost always done by men. With 98. 5% of carpenters being male, it was the fourth most male-dominated occupation in the country in 1999, Carpenters are usually the first tradesmen on a job and the last to leave. Carpenters normally framed post-and-beam buildings until the end of the 19th century and it is also common that the skill can be learned by gaining work experience other than a formal training program, which may be the case in many places. The word carpenter is the English rendering of the Old French word carpentier which is derived from the Latin carpentrius, the Middle English and Scots word was wright, which could be used in compound forms such as wheelwright or boatwright. An easy way to envisage this is that first fix work is all that is done before plastering takes place, second fix is done after plastering takes place. Second fix work, the construction of such as skirting boards, architraves. Carpentry is also used to construct the formwork into which concrete is poured during the building of such as roads. In the UK, the skill of making timber formwork for poured, or in situ, although the. work of a carpenter and joiner are often combined. Joiner is less common than the finish carpenter or cabinetmaker. The terms housewright and barnwright were used historically, now used by carpenters who work using traditional methods. Someone who builds custom concrete formwork is a form carpenter, wood is one of mankinds oldest building materials. The ability to shape wood improved with technological advances from the age to the bronze age to the iron age. The oldest surviving, complete text is Vitruvius ten books collectively titled De architectura which discusses some carpentry. By the 16th century sawmills were coming into use in Europe, the founding of America was partly based on a desire to extract resources from the new continent including wood for use in ships and buildings in Europe. In the 18th century part of the Industrial Revolution was the invention of the steam engine and these technologies combined with the invention of the circular saw led to the development of balloon framing which was the beginning of the decline of traditional timber framing. The 19th century saw the development of engineering and distribution which allowed the development of hand-held power tools, wire nails. In the 20th century portland cement came into use and concrete foundations allowed carpenters to do away with heavy timber sills. Also, drywall came into common use replacing lime plaster on wooden lath, plywood, engineered lumber and chemically treated lumber also came into use
2.
Right angle
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In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two adjacent parts of a straight line. More precisely, if a ray is placed so that its endpoint is on a line, as a rotation, a right angle corresponds to a quarter turn. The presence of an angle in a triangle is the defining factor for right triangles. The term is a calque of Latin angulus rectus, here rectus means upright, in Unicode, the symbol for a right angle is U+221F ∟ Right angle. It should not be confused with the similarly shaped symbol U+231E ⌞ Bottom left corner, related symbols are U+22BE ⊾ Right angle with arc, U+299C ⦜ Right angle variant with square, and U+299D ⦝ Measured right angle with dot. The symbol for an angle, an arc, with a dot, is used in some European countries, including German-speaking countries and Poland. Right angles are fundamental in Euclids Elements and they are defined in Book 1, definition 10, which also defines perpendicular lines. Euclid uses right angles in definitions 11 and 12 to define acute angles, two angles are called complementary if their sum is a right angle. Book 1 Postulate 4 states that all angles are equal. Euclids commentator Proclus gave a proof of this using the previous postulates. Saccheri gave a proof as well but using a more explicit assumption, in Hilberts axiomatization of geometry this statement is given as a theorem, but only after much groundwork. A right angle may be expressed in different units, 1/4 turn, 90° π/2 radians 100 grad 8 points 6 hours Throughout history carpenters and masons have known a quick way to confirm if an angle is a true right angle. It is based on the most widely known Pythagorean triple and so called the Rule of 3-4-5 and this measurement can be made quickly and without technical instruments. The geometric law behind the measurement is the Pythagorean theorem, Thales theorem states that an angle inscribed in a semicircle is a right angle. Two application examples in which the angle and the Thales theorem are included. Cartesian coordinate system Orthogonality Perpendicular Rectangle Types of angles Wentworth, G. A, Euclid, commentary and trans. by T. L. Heath Elements Vol.1 Google Books
3.
Steel
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Steel is an alloy of iron and other elements, primarily carbon, that is widely used in construction and other applications because of its high tensile strength and low cost. Steels base metal is iron, which is able to take on two forms, body centered cubic and face centered cubic, depending on its temperature. It is the interaction of those allotropes with the elements, primarily carbon. In the body-centred cubic arrangement, there is an atom in the centre of each cube. Carbon, other elements, and inclusions within iron act as hardening agents that prevent the movement of dislocations that otherwise occur in the lattices of iron atoms. The carbon in steel alloys may contribute up to 2. 1% of its weight. Steels strength compared to pure iron is possible at the expense of irons ductility. With the invention of the Bessemer process in the mid-19th century and this was followed by Siemens-Martin process and then Gilchrist-Thomas process that refined the quality of steel. With their introductions, mild steel replaced wrought iron, further refinements in the process, such as basic oxygen steelmaking, largely replaced earlier methods by further lowering the cost of production and increasing the quality of the product. Today, steel is one of the most common materials in the world and it is a major component in buildings, infrastructure, tools, ships, automobiles, machines, appliances, and weapons. Modern steel is generally identified by various grades defined by assorted standards organizations, the noun steel originates from the Proto-Germanic adjective stakhlijan, which is related to stakhla. The carbon content of steel is between 0. 002% and 2. 1% by weight for plain iron–carbon alloys and these values vary depending on alloying elements such as manganese, chromium, nickel, iron, tungsten, carbon and so on. Basically, steel is an alloy that does not undergo eutectic reaction. In contrast, cast iron does undergo eutectic reaction, too little carbon content leaves iron quite soft, ductile, and weak. Carbon contents higher than those of steel make an alloy, commonly called pig iron, while iron alloyed with carbon is called carbon steel, alloy steel is steel to which other alloying elements have been intentionally added to modify the characteristics of steel. Common alloying elements include, manganese, nickel, chromium, molybdenum, boron, titanium, vanadium, tungsten, cobalt, and niobium. Additional elements are important in steel, phosphorus, sulfur, silicon, and traces of oxygen, nitrogen, and copper. Alloys with a higher than 2. 1% carbon content, depending on other element content, cast iron is not malleable even when hot, but it can be formed by casting as it has a lower melting point than steel and good castability properties
4.
Angle
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In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane, Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation and this measure is the ratio of the length of a circular arc to its radius. In the case of an angle, the arc is centered at the vertex. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. The word angle comes from the Latin word angulus, meaning corner, cognate words are the Greek ἀγκύλος, meaning crooked, curved, both are connected with the Proto-Indo-European root *ank-, meaning to bend or bow. Euclid defines a plane angle as the inclination to each other, in a plane, according to Proclus an angle must be either a quality or a quantity, or a relationship. In mathematical expressions, it is common to use Greek letters to serve as variables standing for the size of some angle, lower case Roman letters are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples, in geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB, sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex. However, in geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant. Otherwise, a convention may be adopted so that ∠BAC always refers to the angle from B to C. Angles smaller than an angle are called acute angles. An angle equal to 1/4 turn is called a right angle, two lines that form a right angle are said to be normal, orthogonal, or perpendicular. Angles larger than an angle and smaller than a straight angle are called obtuse angles. An angle equal to 1/2 turn is called a straight angle, Angles larger than a straight angle but less than 1 turn are called reflex angles
5.
Aluminium
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Aluminium or aluminum is a chemical element in the boron group with symbol Al and atomic number 13. It is a silvery-white, soft, nonmagnetic, ductile metal, Aluminium metal is so chemically reactive that native specimens are rare and limited to extreme reducing environments. Instead, it is combined in over 270 different minerals. The chief ore of aluminium is bauxite, Aluminium is remarkable for the metals low density and its ability to resist corrosion through the phenomenon of passivation. Aluminium and its alloys are vital to the industry and important in transportation and structures, such as building facades. The oxides and sulfates are the most useful compounds of aluminium, despite its prevalence in the environment, no known form of life uses aluminium salts metabolically, but aluminium is well tolerated by plants and animals. Because of these salts abundance, the potential for a role for them is of continuing interest. Aluminium is a soft, durable, lightweight, ductile. It is nonmagnetic and does not easily ignite, a fresh film of aluminium serves as a good reflector of visible light and an excellent reflector of medium and far infrared radiation. The yield strength of aluminium is 7–11 MPa, while aluminium alloys have yield strengths ranging from 200 MPa to 600 MPa. Aluminium has about one-third the density and stiffness of steel and it is easily machined, cast, drawn and extruded. Aluminium atoms are arranged in a cubic structure. Aluminium has an energy of approximately 200 mJ/m2. Aluminium is a thermal and electrical conductor, having 59% the conductivity of copper. Aluminium is capable of superconductivity, with a critical temperature of 1.2 kelvin. Aluminium is the most common material for the fabrication of superconducting qubits, the strongest aluminium alloys are less corrosion resistant due to galvanic reactions with alloyed copper. This corrosion resistance is reduced by aqueous salts, particularly in the presence of dissimilar metals. In highly acidic solutions, aluminium reacts with water to form hydrogen, primarily because it is corroded by dissolved chlorides, such as common sodium chloride, household plumbing is never made from aluminium
6.
Polymer
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A polymer is a large molecule, or macromolecule, composed of many repeated subunits. Because of their range of properties, both synthetic and natural polymers play an essential and ubiquitous role in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure, Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. The units composing polymers derive, actually or conceptually, from molecules of low molecular mass. The term was coined in 1833 by Jöns Jacob Berzelius, though with a distinct from the modern IUPAC definition. The modern concept of polymers as covalently bonded macromolecular structures was proposed in 1920 by Hermann Staudinger, Polymers are studied in the fields of biophysics and macromolecular science, and polymer science. Polyisoprene of latex rubber is an example of a polymer. In biological contexts, essentially all biological macromolecules—i. e, proteins, nucleic acids, and polysaccharides—are purely polymeric, or are composed in large part of polymeric components—e. g. Isoprenylated/lipid-modified glycoproteins, where small molecules and oligosaccharide modifications occur on the polyamide backbone of the protein. The simplest theoretical models for polymers are ideal chains, Polymers are of two types, Natural polymeric materials such as shellac, amber, wool, silk and natural rubber have been used for centuries. A variety of natural polymers exist, such as cellulose. Most commonly, the continuously linked backbone of a used for the preparation of plastics consists mainly of carbon atoms. A simple example is polyethylene, whose repeating unit is based on ethylene monomer, however, other structures do exist, for example, elements such as silicon form familiar materials such as silicones, examples being Silly Putty and waterproof plumbing sealant. Oxygen is also present in polymer backbones, such as those of polyethylene glycol, polysaccharides. Polymerization is the process of combining many small molecules known as monomers into a covalently bonded chain or network, during the polymerization process, some chemical groups may be lost from each monomer. This is the case, for example, in the polymerization of PET polyester, the distinct piece of each monomer that is incorporated into the polymer is known as a repeat unit or monomer residue. Laboratory synthetic methods are divided into two categories, step-growth polymerization and chain-growth polymerization. However, some methods such as plasma polymerization do not fit neatly into either category
7.
Inch
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The inch is a unit of length in the imperial and United States customary systems of measurement now formally equal to 1⁄36 yard but usually understood as 1⁄12 of a foot. Derived from the Roman uncia, inch is also used to translate related units in other measurement systems. The English word inch was a borrowing from Latin uncia not present in other Germanic languages. The vowel change from Latin /u/ to English /ɪ/ is known as umlaut, the consonant change from the Latin /k/ to English /tʃ/ or /ʃ/ is palatalisation. Both were features of Old English phonology, inch is cognate with ounce, whose separate pronunciation and spelling reflect its reborrowing in Middle English from Anglo-Norman unce and ounce. In many other European languages, the word for inch is the same as or derived from the word for thumb, the inch is a commonly used customary unit of length in the United States, Canada, and the United Kingdom. It is also used in Japan for electronic parts, especially display screens, for example, three feet two inches can be written as 3′ 2″. Paragraph LXVII sets out the fine for wounds of various depths, one inch, one shilling, an Anglo-Saxon unit of length was the barleycorn. After 1066,1 inch was equal to 3 barleycorns, which continued to be its legal definition for several centuries, similar definitions are recorded in both English and Welsh medieval law tracts. One, dating from the first half of the 10th century, is contained in the Laws of Hywel Dda which superseded those of Dyfnwal, both definitions, as recorded in Ancient Laws and Institutes of Wales, are that three lengths of a barleycorn is the inch. However, the oldest surviving manuscripts date from the early 14th century, john Bouvier similarly recorded in his 1843 law dictionary that the barleycorn was the fundamental measure. He noted that this process would not perfectly recover the standard, before the adoption of the international yard and pound, various definitions were in use. In the United Kingdom and most countries of the British Commonwealth, the United States adopted the conversion factor 1 metre =39.37 inches by an act in 1866. In 1930, the British Standards Institution adopted an inch of exactly 25.4 mm, the American Standards Association followed suit in 1933. By 1935, industry in 16 countries had adopted the industrial inch as it came to be known, in 1946, the Commonwealth Science Congress recommended a yard of exactly 0.9144 metres for adoption throughout the British Commonwealth. This was adopted by Canada in 1951, the United States on 1 July 1959, Australia in 1961, effective 1 January 1964, and the United Kingdom in 1963, effective on 1 January 1964. The new standards gave an inch of exactly 25.4 mm,1.7 millionths of a longer than the old imperial inch and 2 millionths of an inch shorter than the old US inch. The United States retains the 1/39. 37-metre definition for survey purposes and this is approximately 1/8-inch in a mile
8.
Rafter
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A pair of rafters is a couple. A type of beam that supports the roof of a building, in home construction rafters are normally made of wood. Exposed rafters could be a feature of traditional roof styles, there are many names for rafters depending on their location, shape, or size. The earliest surviving roofs in Europe are of common rafters on a tie beam, later principal rafters and common rafters were mixed which is called a major/minor or primary/secondary roof system. Historically many rafters, including hip rafters, often taper in height 1/5 to 1/6 of their width, architect George Woodward discusses the purpose of this in 1860, “The same amount of strength can be had with a less amount of lumber. There is a labor in sawing such rafters, as well as a different calculation to be made in using up a log to the best advantage. It is necessary always to order this special bill of rafters direct from the mill, john Muller also discusses a one-sixth taper for rafters. Pieces added at the feet to create an overhang or change the pitch are called a sprocket or coyau in French. (The projecting piece on the gable of a forming an overhang is called a lookout. A rafter can be reinforced with a strut, principal purlin, collar beam, rafter types include, Principal rafter, A larger rafter. Usually land directly on a tie beam, usually the purpose of having a larger rafter is to carry a purlin which supports the rafters in each bay. Sometimes the top cord of a truss looks like a principal rafter, Principal rafters are sometimes simply called principals. Common rafter, being smaller than a principal rafter, a “principal/common rafter roof” or double roof has both principals and commons. Auxiliary rafter, A secondary rafter below and supporting a principal rafter, compass rafter, A rafter curved or bowed on the top or both the top and bottom surfaces. Curb rafter, The upper rafters in a curb roof, hip rafter, The rafter in the corners of a hip roof. The foot of a hip rafter lands on a dragon beam, king rafter, the longest rafter on the side of a hip roof in line with the ridge. Valley rafter, A rafter forming a valley, intermediate rafter, “one between principal or common rafters to strengthen a given place”. Jack rafter, cripple rafter, cripple-jack rafter, A shortened rafter such as landing on a hip rafter or interrupted by a dormer, arched rafter, Of segmental form in an arched roof
9.
Roof
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A roof is part of a building envelope. It is the covering on the uppermost part of a building or shelter which provides protection from animals and weather, notably rain or snow, the word also denotes the framing or structure which supports that covering. In most countries a roof protects primarily against rain, a verandah may be roofed with material that protects against sunlight but admits the other elements. The roof of a garden conservatory protects plants from cold, wind, and rain, a roof may also provide additional living space, for example a roof garden. Old English hrof roof, ceiling, top, summit, heaven, sky, also figuratively, highest point of something, there are no apparent connections outside the Germanic family. English alone has retained the word in a sense, for which the other languages use forms corresponding to OE. In many parts of the ceramic tiles have been the predominant roofing material for centuries. Other roofing materials include asphalt, coal tar pitch, EPDM rubber, Hypalon, polyurethane foam, PVC, slate, Teflon fabric, TPO, and wood shakes and shingles. The construction of a roof is determined by its method of support and how the space is bridged. The pitch is the angle at which the roof rises from its lowest to highest point, most US domestic architecture, except in very dry regions, has roofs that are sloped, or pitched. Although modern construction such as drainpipes may remove the need for pitch, roofs are pitched for reasons of tradition. So the pitch is dependent upon stylistic factors, and partially to do with practicalities. Some types of roofing, for example thatch, require a steep pitch in order to be waterproof, other types of roofing, for example pantiles, are unstable on a steeply pitched roof but provide excellent weather protection at a relatively low angle. In regions where there is rain, an almost flat roof with a slight run-off provides adequate protection against an occasional downpour. Drainpipes also remove the need for a sloping roof, a person that specializes in roof construction is called a roofer. The shape of roofs differs greatly from region to region, the main factors which influence the shape of roofs are the climate and the materials available for roof structure and the outer covering. The basic shapes of roofs are flat, mono-pitched, gabled, hipped, butterfly, there are many variations on these types. Roofs constructed of sections that are sloped are referred to as pitched roofs
10.
Stairs
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A stairway, staircase, stairwell, flight of stairs, or simply stairs is a construction designed to bridge a large vertical distance by dividing it into smaller vertical distances, called steps. Stairs may be straight, round, or may consist of two or more straight pieces connected at angles, special types of stairs include escalators and ladders. Some alternatives to stairs are elevators, stairlifts and inclined moving walkways as well as stationary inclined sidewalks, a stair, or a stairstep is one step in a flight of stairs. In buildings, stairs is a term applied to a flight of steps between two floors. A stair flight is a run of stairs or steps between landings, a staircase or stairway is one or more flights of stairs leading from one floor to another, and includes landings, newel posts, handrails, balustrades and additional parts. A stairwell is a compartment extending vertically through a building in which stairs are placed. A stair hall is the stairs, landings, hallways, or other portions of the hall through which it is necessary to pass when going from the entrance floor to the other floors of a building. Box stairs are stairs built between walls, usually with no support except the wall strings, Stairs may be in a straight run, leading from one floor to another without a turn or change in direction. Stairs may change direction, commonly by two flights connected at a 90 degree angle landing. Stairs may also return onto themselves with 180 degree angle landings at each end of straight flights forming a vertical stairway commonly used in multistory, many variations of geometrical stairs may be formed of circular, elliptical and irregular constructions. Stairs may be a component of egress from structures and buildings. Stairs are also provided for convenience to access floors, roofs, levels, Stairs may also be a fanciful physical construct such as the stairs that go nowhere located at the Winchester Mystery House. Stairs are also a used in art to represent real or imaginary places built around impossible objects using geometric distortion. Stairway is also a metaphor for achievement or loss of a position in the society. Each step is composed of tread and riser, tread The part of the stairway that is stepped on. It is constructed to the specifications as any other flooring. The tread depth is measured from the edge of the step to the vertical riser between steps. The width is measured from one side to the other, riser The vertical portion between each tread on the stair
11.
Diagonal
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In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal, in matrix algebra, a diagonal of a square matrix is a set of entries extending from one corner to the farthest corner. There are also other, non-mathematical uses, diagonal pliers are wire-cutting pliers defined by the cutting edges of the jaws intersects the joint rivet at an angle or on a diagonal, hence the name. A diagonal lashing is a type of lashing used to bind spars or poles together applied so that the cross over the poles at an angle. In association football, the system of control is the method referees. As applied to a polygon, a diagonal is a line segment joining any two non-consecutive vertices, therefore, a quadrilateral has two diagonals, joining opposite pairs of vertices. For any convex polygon, all the diagonals are inside the polygon, in a convex polygon, if no three diagonals are concurrent at a single point, the number of regions that the diagonals divide the interior into is given by + =24. The number of regions is 1,4,11,25,50,91,154,246, in a polygon with n angles the number of diagonals is given by n ∗2. The number of intersections between the diagonals is given by, in the case of a square matrix, the main or principal diagonal is the diagonal line of entries running from the top-left corner to the bottom-right corner. For a matrix A with row index specified by i and column index specified by j, the off-diagonal entries are those not on the main diagonal. A diagonal matrix is one whose off-diagonal entries are all zero, a superdiagonal entry is one that is directly above and to the right of the main diagonal. Just as diagonal entries are those A i j with j = i and this plays an important part in geometry, for example, the fixed points of a mapping F from X to itself may be obtained by intersecting the graph of F with the diagonal. In geometric studies, the idea of intersecting the diagonal with itself is common, not directly and this is related at a deep level with the Euler characteristic and the zeros of vector fields. For example, the circle S1 has Betti numbers 1,1,0,0,0, a geometric way of expressing this is to look at the diagonal on the two-torus S1xS1 and observe that it can move off itself by the small motion to. Topics In Algebra, Waltham, Blaisdell Publishing Company, ISBN 978-1114541016 Nering, linear Algebra and Matrix Theory, New York, Wiley, LCCN76091646 Diagonals of a polygon with interactive animation Polygon diagonal from MathWorld. Diagonal of a matrix from MathWorld
12.
Octagon
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In geometry, an octagon is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol and can also be constructed as a truncated square, t. A truncated octagon, t is a hexadecagon, t, the sum of all the internal angles of any octagon is 1080°. As with all polygons, the external angles total 360°, the midpoint octagon of a reference octagon has its eight vertices at the midpoints of the sides of the reference octagon. A regular octagon is a figure with sides of the same length. It has eight lines of symmetry and rotational symmetry of order 8. A regular octagon is represented by the Schläfli symbol, the internal angle at each vertex of a regular octagon is 135°. The area of an octagon of side length a is given by A =2 cot π8 a 2 =2 a 2 ≃4.828 a 2. In terms of the circumradius R, the area is A =4 sin π4 R2 =22 R2 ≃2.828 R2. In terms of the r, the area is A =8 tan π8 r 2 =8 r 2 ≃3.314 r 2. These last two coefficients bracket the value of pi, the area of the unit circle. The area can also be expressed as A = S2 − a 2, where S is the span of the octagon, or the second-shortest diagonal, and a is the length of one of the sides, or bases. This is easily proven if one takes an octagon, draws a square around the outside and then takes the corner triangles and places them with right angles pointed inward, the edges of this square are each the length of the base. Given the length of a side a, the span S is S = a 2 + a + a 2 = a ≈2.414 a. The area is then as above, A =2 − a 2 =2 a 2 ≈4.828 a 2, expressed in terms of the span, the area is A =2 S2 ≈0.828 S2. Another simple formula for the area is A =2 a S, more often the span S is known, and the length of the sides, a, is to be determined, as when cutting a square piece of material into a regular octagon. From the above, a ≈ S /2.414, the two end lengths e on each side, as well as being e = a /2, may be calculated as e = /2. The circumradius of the octagon in terms of the side length a is R = a
13.
Winding stick
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In woodworking and carpentry, a pair of winding sticks is a tool that aids in viewing twist or wind in pieces of lumber by amplifying the defect. Winding sticks can be as simple as any two straight sticks or they can be elegant, decorated, dimensionally stable wood like mahogany, a pair of framing squares may also be suitable. Traditionally they are 16 inches to 30 inches long 1.75 inches tall, the longer the winding sticks, the more they will amplify the wind. One winding stick is placed on one end of the piece and the second winding stick is placed on the other end, the woodworker then stands back a short distance and sights across the top of the two sticks. If the surface on which the sticks are sitting is flat, adjustments to the surface of the board are then made. This process is repeated all across the piece until the piece is satisfactorily true, longitudinally the piece is checked with a straightedge
14.
Timber frame
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Timber framing and post-and-beam construction are methods of building with heavy timbers rather than dimensional lumber such as 2x4s. Traditional timber framing is the method of creating structures using heavy squared-off and it is commonplace in wooden buildings from the 19th century and earlier. The method comes from making out of logs and tree trunks without modern high tech saws to cut lumber from the starting material stock. Since this building method has been used for thousands of years in parts of the world. These styles are categorized by the type of foundation, walls, how and where the beams intersect, the use of curved timbers. Three basic types of frames in English-speaking countries are the box frame, cruck frame. The distinction presented here is the load is carried by the exterior walls. Purlins are also in a timber frame. A cruck is a pair of crooked or curved timbers which form a bent or crossframe, more than 4,000 cruck frame buildings have been recorded in the UK. Several types of frames are used, more information follows in English style below. True cruck or full cruck, blades, straight or curved, base cruck, tops of the blades are truncated by the first transverse member such as by a tie beam. Raised cruck, blades land on masonry wall, and extend to the ridge, middle cruck, blades land on masonry wall, and are truncated by a collar. Upper cruck, blades land on a tie beam, very similar to knee rafters, jointed cruck, blades are made from pieces joined near eaves in a number of ways. See also, hammerbeam roof End cruck is not a style, aisled frames have one or more rows of interior posts. These interior posts typically carry more load than the posts in the exterior walls. This is the concept of the aisle in church buildings, sometimes called a hall church. However, a nave is often called an aisle, and three-aisled barns are common in the U. S. the Netherlands, aisled buildings are wider than the simpler box-framed or cruck-framed buildings, and typically have purlins supporting the rafters. In northern Germany, this construction is known as variations of a Ständerhaus, the frame is often left exposed on the exterior of the building
15.
Mortise and tenon
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The mortise and tenon joint has been used for thousands of years by woodworkers around the world to join pieces of wood, mainly when the adjoining pieces connect at an angle of 90°. In its basic form it is simple and strong. Although there are many joint variations, the mortise and tenon comprises two components, the mortise hole and the tenon tongue. The tenon, formed on the end of a member generally referred to as a rail, is inserted into a square or rectangular hole cut into the corresponding member. The tenon is cut to fit the hole exactly and usually has shoulders that seat when the joint fully enters the mortise hole. The joint may be glued, pinned, or wedged to lock it in place and this joint is also used with other materials. For example, it is a method for stonemasons and blacksmiths. A mortise is a cavity cut into a timber to receive a tenon, there are several kinds of mortise, Open mortise a mortise that has only three sides. Stub mortise a mortise, the depth of which depends on the size of the timber. Through mortise a mortise that passes entirely through a piece, wedged half-dovetail a mortise in which the back is wider, or taller, than the front, or opening. The space for the wedge initially allows room for the tenon to be inserted and it is sometimes called a suicide joint, since it is a one-way trip. Through-wedged half-dovetail a wedged half-dovetail mortise that passes entirely through the piece, a tenon is a projection on the end of a timber for insertion into a mortise. Usually the tenon is taller than it is wide. There are several kinds of tenon, Stub tenon short, the depth of which depends on the size of the timber, through tenon a tenon that passes entirely through the piece of wood it is inserted into, being clearly visible on the back side. Loose tenon a tenon that is a part of the joint. Teasel tenon a term used for the tenon on top of a jowled or gunstock post, a common element of the English tying joint. Top tenon the tenon that occurs on top of a post, hammer-headed tenon a method of forming a tenon joint when the shoulders cannot be tightened with a clamp. Half shoulder tenon An asymmetric tenon with a shoulder on one side only, a common use is in framed, ledged and braced doors
16.
Stair riser
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A stair riser is the near-vertical element in a set of stairs, forming the space between one step and the next. It is sometimes slightly inclined from the vertical so that its top is closer than its base to the climbing the stairs. The horizontal edge of the stair is called the nosing, whereas the surface on which a whole foot makes contact is called the tread. Decorated stair risers were used extensively in the Greco-Buddhist art of Gandhara and they were usually adorned with friezes, fantastic animals and decorations. A flight of stairs with decorated stair risers from the Chakhil-i-Ghoundi Stupa has been almost fully restored and can now be seen at the Guimet Museum in Paris
17.
Lumber
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Lumber, or timber is wood that has been processed into beams and planks, a stage in the process of wood production. Lumber may also refer to currently un-needed furniture, as in Lumber room, or an awkward gait, ultimately derived from the look of unfashionable, Lumber may be supplied either rough-sawn, or surfaced on one or more of its faces. Besides pulpwood, rough lumber is the raw material for furniture-making and it is available in many species, usually hardwoods, but it is also readily available in softwoods, such as white pine and red pine, because of their low cost. Lumber is mainly used for structural purposes but has other uses as well. It is classified more commonly as a softwood than as a hardwood, in Australia, Ireland, New Zealand and Britain, the term timber describes sawn wood products, such as floor boards. In the United States and Canada, generally timber describes standing or felled trees, before they are milled into boards, Timber there also describes sawn lumber not less than 5 inches in its smallest dimension. The latter includes the often partly finished lumber used in timber-frame construction, remanufactured lumber is the result of secondary or tertiary processing/cutting of previously milled lumber. Specifically, it is cut for industrial or wood-packaging use. Lumber is cut by ripsaw or resaw to create dimensions that are not usually processed by a primary sawmill, resawing is the splitting of 1-inch through 12-inch hardwood or softwood lumber into two or more thinner pieces of full-length boards. For example, splitting a ten-foot 2×4 into two ten-foot 1×4s is considered resawing, structural lumber may also be produced from recycled plastic and new plastic stock. Its introduction has been opposed by the forestry industry. Blending fiberglass in plastic lumber enhances its strength, durability, logs are converted into timber by being sawn, hewn, or split. Sawing with a rip saw is the most common method, because sawing allows logs of lower quality, with grain and large knots. There are various types of sawing, Plain sawn —A log sawn through without adjusting the position of the log, quarter sawn and rift sawn—These terms have been confused in history but generally mean lumber sawn so the annual rings are reasonably perpendicular to the sides of the lumber. Boxed heart—The pith remains within the piece with some allowance for exposure, heart center—the center core of a log. Free of heart center —A side-cut timber without any pith, free of knots —No knots are present. Dimensional lumber is lumber that is cut to standardized width and depth, carpenters extensively use dimensional lumber in framing wooden buildings. Common sizes include 2×4, 2×6, and 4×4, the length of a board is usually specified separately from the width and depth
18.
Pythagorean theorem
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In mathematics, the Pythagorean theorem, also known as Pythagorass theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse is equal to the sum of the squares of the two sides. There is some evidence that Babylonian mathematicians understood the formula, although little of it indicates an application within a mathematical framework, Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases. The theorem has been given numerous proofs – possibly the most for any mathematical theorem and they are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The Pythagorean theorem was known long before Pythagoras, but he may well have been the first to prove it, in any event, the proof attributed to him is very simple, and is called a proof by rearrangement. The two large squares shown in the figure each contain four triangles, and the only difference between the two large squares is that the triangles are arranged differently. Therefore, the space within each of the two large squares must have equal area. Equating the area of the white space yields the Pythagorean theorem and that Pythagoras originated this very simple proof is sometimes inferred from the writings of the later Greek philosopher and mathematician Proclus. Several other proofs of this theorem are described below, but this is known as the Pythagorean one, If the length of both a and b are known, then c can be calculated as c = a 2 + b 2. If the length of the c and of one side are known. The Pythagorean equation relates the sides of a triangle in a simple way. Another corollary of the theorem is that in any triangle, the hypotenuse is greater than any one of the other sides. A generalization of this theorem is the law of cosines, which allows the computation of the length of any side of any triangle, If the angle between the other sides is a right angle, the law of cosines reduces to the Pythagorean equation. This theorem may have more known proofs than any other, the book The Pythagorean Proposition contains 370 proofs, Let ABC represent a right triangle, with the right angle located at C, as shown on the figure. Draw the altitude from point C, and call H its intersection with the side AB, point H divides the length of the hypotenuse c into parts d and e. By a similar reasoning, the triangle CBH is also similar to ABC, the proof of similarity of the triangles requires the triangle postulate, the sum of the angles in a triangle is two right angles, and is equivalent to the parallel postulate. Similarity of the leads to the equality of ratios of corresponding sides. The first result equates the cosines of the angles θ, whereas the second result equates their sines, the role of this proof in history is the subject of much speculation
19.
Slope
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In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The direction of a line is increasing, decreasing, horizontal or vertical. A line is increasing if it goes up from left to right, the slope is positive, i. e. m >0. A line is decreasing if it goes down from left to right, the slope is negative, i. e. m <0. If a line is horizontal the slope is zero, if a line is vertical the slope is undefined. The steepness, incline, or grade of a line is measured by the value of the slope. A slope with an absolute value indicates a steeper line Slope is calculated by finding the ratio of the vertical change to the horizontal change between two distinct points on a line. Sometimes the ratio is expressed as a quotient, giving the number for every two distinct points on the same line. A line that is decreasing has a negative rise, the line may be practical - as set by a road surveyor, or in a diagram that models a road or a roof either as a description or as a plan. The rise of a road between two points is the difference between the altitude of the road at two points, say y1 and y2, or in other words, the rise is = Δy. Here the slope of the road between the two points is described as the ratio of the altitude change to the horizontal distance between any two points on the line. In mathematical language, the m of the line is m = y 2 − y 1 x 2 − x 1. The concept of slope applies directly to grades or gradients in geography, as a generalization of this practical description, the mathematics of differential calculus defines the slope of a curve at a point as the slope of the tangent line at that point. When the curve given by a series of points in a diagram or in a list of the coordinates of points, thereby, the simple idea of slope becomes one of the main basis of the modern world in terms of both technology and the built environment. This is described by the equation, m = Δ y Δ x = vertical change horizontal change = rise run. Given two points and, the change in x from one to the other is x2 − x1, substituting both quantities into the above equation generates the formula, m = y 2 − y 1 x 2 − x 1. The formula fails for a line, parallel to the y axis. Suppose a line runs through two points, P = and Q =, since the slope is positive, the direction of the line is increasing
20.
Roof pitch
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In building construction, roof pitch is a numerical measure of the steepness of a roof. Roofs may be flat or pitched. The pitch of a roof is its vertical rise divided by its horizontal span, what is called slope in geometry and stair construction, in the imperial measurement systems it is typically expressed with the rise first and run second. In the USA, the run is denominated by the number 12, for example,3,12,4,12,5,12, and so on. Countries which use metric measurement systems use an angle, or what fall there is per unit of run, and expressed as a 1 in x slope. Where convenient, the LCMs are used, e. g. a 3 in 4 slope, rather than 9, US convention is to use whole numbers when even or the nearest single or two-digit fraction when not. Definitions vary on when a roof is considered pitched, in degrees, 10° is considered a minimum. The exact roof slope in degrees is given by the arctangent, for example, arctan=14. 0° The primary purpose of pitching a roof is to redirect water and snow. Thus, pitch is greater in areas of high rain or snowfall. The steep roof of the tropical Papua New Guinea longhouse, for example, the high, steeply-pitched gabled roofs of northern Europe are typical in regions of heavy snowfall. In some areas building codes require a minimum slope, buffalo, New York and Montreal, Quebec, Canada, specify 6 in 12, a pitch of approximately 26.6 degrees. Carpenters frame rafters on an angle to pitch a roof, gable and other multi-pitched roofs allow for lower primary structures with a corresponding reduction in framing and sheathing materials. Historically roof pitch was designated in two ways, A ratio of the ridge height to the width of the building. List of roof shapes Mono-pitched roof How to determine roof pitch Roof pitch calculator
21.
Hypotenuse
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In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite of the right angle. For example, if one of the sides has a length of 3. The length of the hypotenuse is the root of 25. The word ὑποτείνουσα was used for the hypotenuse of a triangle by Plato in the Timaeus 54d, a folk etymology says that tenuse means side, so hypotenuse means a support like a prop or buttress, but this is inaccurate. The length of the hypotenuse is calculated using the square root function implied by the Pythagorean theorem. Using the common notation that the length of the two legs of the triangle are a and b and that of the hypotenuse is c, many computer languages support the ISO C standard function hypot, which returns the value above. The function is designed not to fail where the straightforward calculation might overflow or underflow, some scientific calculators provide a function to convert from rectangular coordinates to polar coordinates. This gives both the length of the hypotenuse and the angle the hypotenuse makes with the line at the same time when given x and y. The angle returned will normally be given by atan2. Orthographic projections, The length of the hypotenuse equals the sum of the lengths of the projections of both catheti. And The square of the length of a cathetus equals the product of the lengths of its projection on the hypotenuse times the length of this. Given the length of the c and of a cathetus b. The adjacent angle of the b, will be α = 90° – β One may also obtain the value of the angle β by the equation. Cathetus Triangle Space diagonal Nonhypotenuse number Taxicab geometry Trigonometry Special right triangles Pythagoras Hypotenuse at Encyclopaedia of Mathematics Weisstein, Eric W. Hypotenuse
22.
Horizontal plane
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Alternatively, a spirit level, which exploits the buoyancy of a bubble, can be used to determine if the plane is horizontal. In radio science, horizontal plane is used to plot an antennas relative field strength in relation to the ground on a polar graph. Normally the maximum of 1.000 or 0 dB is at the top, other field strengths are expressed as a decimal less than 1.000, a percentage less than 100%, or decibels less than 0 dB. If the graph is of an actual or proposed installation, rotation is applied so that the top is 0o true north, see also the perpendicular vertical plane. In general, something that is horizontal can be drawn from left to right, although the word horizontal is commonly used in daily life and language, it is subject to many misconceptions. The concept of horizontality only makes sense in the context of a clearly measurable gravity field, i. e. in the neighborhood of a planet, star, when the gravity field becomes very weak, the notion of being horizontal loses its meaning. A plane is only at the chosen point. Horizontal planes at two points are not parallel, they intersect. Thus both horizontality and verticality are strictly speaking local concepts, and it is necessary to state to which location the direction or the plane refers to. In reality, the gravity field of a planet such as Earth is deformed due to the inhomogeneous spatial distribution of materials with different densities. Actual horizontal planes are not even parallel even if their reference points are along the same vertical line. At any given location, the gravitational force is not quite constant over time. For instance, on Earth the horizontal plane at a given point changes with the position of the Moon. On a rotating planet such as Earth, the gravitational pull of the planet is different from the apparent net force that can be measured in the laboratory or in the field. This difference is the force associated with the planets rotation. This is a force, it only arises when calculations or experiments are conducted in non-inertial frames of reference. Hence, the world appears to be flat locally, and horizontal planes in nearby locations appear to be parallel, such statements are nevertheless approximations, whether they are acceptable in any particular context or application depends on the applicable requirements, in particular in terms of accuracy. In this case, the direction is typically from the left side of the paper to the right side
23.
Timber framing
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Timber framing and post-and-beam construction are methods of building with heavy timbers rather than dimensional lumber such as 2x4s. Traditional timber framing is the method of creating structures using heavy squared-off and it is commonplace in wooden buildings from the 19th century and earlier. The method comes from making out of logs and tree trunks without modern high tech saws to cut lumber from the starting material stock. Since this building method has been used for thousands of years in parts of the world. These styles are categorized by the type of foundation, walls, how and where the beams intersect, the use of curved timbers. Three basic types of frames in English-speaking countries are the box frame, cruck frame. The distinction presented here is the load is carried by the exterior walls. Purlins are also in a timber frame. A cruck is a pair of crooked or curved timbers which form a bent or crossframe, more than 4,000 cruck frame buildings have been recorded in the UK. Several types of frames are used, more information follows in English style below. True cruck or full cruck, blades, straight or curved, base cruck, tops of the blades are truncated by the first transverse member such as by a tie beam. Raised cruck, blades land on masonry wall, and extend to the ridge, middle cruck, blades land on masonry wall, and are truncated by a collar. Upper cruck, blades land on a tie beam, very similar to knee rafters, jointed cruck, blades are made from pieces joined near eaves in a number of ways. See also, hammerbeam roof End cruck is not a style, aisled frames have one or more rows of interior posts. These interior posts typically carry more load than the posts in the exterior walls. This is the concept of the aisle in church buildings, sometimes called a hall church. However, a nave is often called an aisle, and three-aisled barns are common in the U. S. the Netherlands, aisled buildings are wider than the simpler box-framed or cruck-framed buildings, and typically have purlins supporting the rafters. In northern Germany, this construction is known as variations of a Ständerhaus, the frame is often left exposed on the exterior of the building
24.
Calculator
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An electronic calculator is a small, portable electronic device used to perform operations ranging from basic arithmetic to complex mathematics. The first solid state electronic calculator was created in the 1960s, building on the history of tools such as the abacus. It was developed in parallel with the computers of the day. The pocket sized devices became available in the 1970s, especially after the first microprocessor and they later became used commonly within the petroleum industry. Modern electronic calculators vary, from cheap, give-away, credit-card-sized models to sturdy desktop models with built-in printers and they became popular in the mid-1970s. By the end of decade, calculator prices had reduced to a point where a basic calculator was affordable to most. In addition to general purpose calculators, there are designed for specific markets. For example, there are scientific calculators which include trigonometric and statistical calculations, some calculators even have the ability to do computer algebra. Graphing calculators can be used to graph functions defined on the real line, as of 2016, basic calculators cost little, but the scientific and graphing models tend to cost more. In 1986, calculators still represented an estimated 41% of the worlds general-purpose hardware capacity to compute information, by 2007, this diminished to less than 0. 05%. Modern 2016 electronic calculators contain a keyboard with buttons for digits and arithmetical operations, most basic calculators assign only one digit or operation on each button, however, in more specific calculators, a button can perform multi-function working with key combinations. Large-sized figures and comma separators are used to improve readability. Various symbols for function commands may also be shown on the display, fractions such as 1⁄3 are displayed as decimal approximations, for example rounded to 0.33333333. Also, some fractions can be difficult to recognize in decimal form, as a result, Calculators also have the ability to store numbers into computer memory. Basic types of these only one number at a time. The variables can also be used for constructing formulas, some models have the ability to extend memory capacity to store more numbers, the extended memory address is termed an array index. Power sources of calculators are, batteries, solar cells or mains electricity, some models even have no turn-off button but they provide some way to put off. Crank-powered calculators were also common in the computer era
25.
Right triangle
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A right triangle or right-angled triangle is a triangle in which one angle is a right angle. The relation between the sides and angles of a triangle is the basis for trigonometry. The side opposite the angle is called the hypotenuse. The sides adjacent to the angle are called legs. Side a may be identified as the adjacent to angle B and opposed to angle A, while side b is the side adjacent to angle A. If the lengths of all three sides of a triangle are integers, the triangle is said to be a Pythagorean triangle. As with any triangle, the area is equal to one half the base multiplied by the corresponding height. In a right triangle, if one leg is taken as the then the other is height. As a formula the area T is T =12 a b where a and b are the legs of the triangle and this formula only applies to right triangles. From this, The altitude to the hypotenuse is the mean of the two segments of the hypotenuse. Each leg of the triangle is the mean proportional of the hypotenuse, in equations, f 2 = d e, b 2 = c e, a 2 = c d where a, b, c, d, e, f are as shown in the diagram. Moreover, the altitude to the hypotenuse is related to the legs of the triangle by 1 a 2 +1 b 2 =1 f 2. For solutions of this equation in integer values of a, b, f, the altitude from either leg coincides with the other leg. Since these intersect at the vertex, the right triangles orthocenter—the intersection of its three altitudes—coincides with the right-angled vertex. The Pythagorean theorem states that, In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs. This can be stated in equation form as a 2 + b 2 = c 2 where c is the length of the hypotenuse, Pythagorean triples are integer values of a, b, c satisfying this equation. The radius of the incircle of a triangle with legs a and b. The radius of the circumcircle is half the length of the hypotenuse, thus the sum of the circumradius and the inradius is half the sum of the legs, R + r = a + b 2
26.
Cathetus
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In a right triangle, a cathetus, commonly known as a leg, is either of the sides that are adjacent to the right angle. It is occasionally called a side about the right angle, the side opposite the right angle is the hypotenuse. In the context of the hypotenuse, the catheti are sometimes referred to simply as the two sides. If the catheti of a triangle have equal lengths, the triangle is isosceles. If they have different lengths, a distinction can be made between the minor and major cathetus. In a right triangle, the length of a cathetus is the mean of the length of the adjacent segment cut by the altitude to the hypotenuse. By the Pythagorean theorem, the sum of the squares of the lengths of the catheti is equal to the square of the length of the hypotenuse, geographic Information Systems, An Introduction, 3rd ed. New York, Wiley, p.271,2002, Cathetus at Encyclopaedia of Mathematics Weisstein, Eric W. Cathetus
27.
Inverse trigonometric functions
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In mathematics, the inverse trigonometric functions are the inverse functions of the trigonometric functions. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry. There are several notations used for the trigonometric functions. The most common convention is to name inverse trigonometric functions using a prefix, e. g. arcsin, arccos, arctan. This convention is used throughout the article, when measuring in radians, an angle of θ radians will correspond to an arc whose length is rθ, where r is the radius of the circle. Similarly, in programming languages the inverse trigonometric functions are usually called asin, acos. The notations sin−1, cos−1, tan−1, etc, the confusion is somewhat ameliorated by the fact that each of the reciprocal trigonometric functions has its own name—for example, −1 = sec. Nevertheless, certain authors advise against using it for its ambiguity, since none of the six trigonometric functions are one-to-one, they are restricted in order to have inverse functions. There are multiple numbers y such that sin = x, for example, sin =0, when only one value is desired, the function may be restricted to its principal branch. With this restriction, for x in the domain the expression arcsin will evaluate only to a single value. These properties apply to all the trigonometric functions. The principal inverses are listed in the following table, if x is allowed to be a complex number, then the range of y applies only to its real part. Trigonometric functions of trigonometric functions are tabulated below. This is derived from the tangent addition formula tan = tan + tan 1 − tan tan , like the sine and cosine functions, the inverse trigonometric functions can be calculated using power series, as follows. For arcsine, the series can be derived by expanding its derivative,11 − z 2, as a binomial series, the series for arctangent can similarly be derived by expanding its derivative 11 + z 2 in a geometric series and applying the integral definition above. Arcsin = z + z 33 + z 55 + z 77 + ⋯ = ∑ n =0 ∞, for example, arccos x = π /2 − arcsin x, arccsc x = arcsin , and so on. Alternatively, this can be expressed, arctan z = ∑ n =0 ∞22 n 2. There are two cuts, from −i to the point at infinity, going down the imaginary axis and it works best for real numbers running from −1 to 1
28.
Complementary angle
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In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane, Angles are also formed by the intersection of two planes in Euclidean and other spaces. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles. Angle is also used to designate the measure of an angle or of a rotation and this measure is the ratio of the length of a circular arc to its radius. In the case of an angle, the arc is centered at the vertex. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. The word angle comes from the Latin word angulus, meaning corner, cognate words are the Greek ἀγκύλος, meaning crooked, curved, both are connected with the Proto-Indo-European root *ank-, meaning to bend or bow. Euclid defines a plane angle as the inclination to each other, in a plane, according to Proclus an angle must be either a quality or a quantity, or a relationship. In mathematical expressions, it is common to use Greek letters to serve as variables standing for the size of some angle, lower case Roman letters are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples, in geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB, sometimes, where there is no risk of confusion, the angle may be referred to simply by its vertex. However, in geometrical situations it is obvious from context that the positive angle less than or equal to 180 degrees is meant. Otherwise, a convention may be adopted so that ∠BAC always refers to the angle from B to C. Angles smaller than an angle are called acute angles. An angle equal to 1/4 turn is called a right angle, two lines that form a right angle are said to be normal, orthogonal, or perpendicular. Angles larger than an angle and smaller than a straight angle are called obtuse angles. An angle equal to 1/2 turn is called a straight angle, Angles larger than a straight angle but less than 1 turn are called reflex angles
29.
Speed square
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A Speed Square is a triangular-shaped, carpenters marking out tool manufactured and sold by Swanson Tool Co. Inc. The Speed Square combines some of the most common functions of the square, try square. It is used to make measurements and mark lines on dimensional lumber. A Speed Square is a layout tool invented in 1925 by Albert J. Swanson who later founded Swanson Tool Company. Today, Swanson Tool Co. continues to manufacture and distribute the Speed Square and other tools from its headquarters in Frankfort. SPEED and SPEED SQUARE are also registered trademarks of Swanson Tool Co. Inc, Common lines made using a Speed Square include perpendicular cut marks and angles for roofs, stairways, and decks. Embedded degree gradations on the tool eliminate complex trigonometry, making for speedy lines, variants of the tool made of aluminum, steel, and composites such as HDPE, and come in two basic sizes, the original 7 inch and a 12 inch model for larger tasks. The tool is a triangle with a ruler on one equal side. It is marked with the word Pivot at the right angle point and displays Degrees on its hypotenuse, Common, degree indicate the angle in degrees from 0° to 90°. Common indicate the rise in inches over a 12 inch run for common rafters from 1 inch to 30 inch, Hip/Val indicate the rise in inches over a 17 inch run for Hip or Valley rafters from 1 inch to 30 inch. Some models have divots for fitting a writing utensil to mark lumber with, genuine Swanson Speed® Squares will also have a diamond shape cutout on the ruler side at 3½ inch. Swanson Tool Co. Inc. describes the tool as a Try Square, Miter Square, Protractor, Line Scriber, Swanson Speed Squares come with a pocket sized blue reference book describing the tools functions and containing charts listing rafter lengths for building widths from 3 to 40 feet. Among its basic uses are marking common, hip, valley and hip, or valley jack rafters, laying out stair stringers, determining and marking angles and this tool uses a 0° reference. This means when a board is squared off the tool reads 0°. The angle derived is actually a complementary angle, for example a 22. 5° angle is actually 67. 5°. The sum of the angles equals 90 degrees and it is obvious from a visual check that where the instruments displays 22. 5° is not 22. 5°. Many of the new slide miters and miter boxes display both angles, some of the new calculators have a 0° and a 90° references to do angular calculations. This can create confusion if the user does not understand this angular calibration. Combination square Try square Steel square
30.
Combination square
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A combination square is a tool used for multiple purposes in woodworking, stonemasonry and metalworking. It is composed of a blade and one or more interchangeable heads that may be affixed to it. The most common head is the standard or square head which is used to lay out or check right, invented in 1883 by Laroy S. Starrett, the combination square continues to be a commonplace tool in home workshops, construction jobsites and metalworking. Measuring angles — A combination square can reliably measure 90° and 45° angles, the 45° angle is used commonly in creating miter joints. Determining flatness — When working with wood the first step is to designate a reference surface on a board which is known as the face side, the rest of the workpiece is measured from the face side Measuring the center of a circular bar or dowel. Perform this action at two locations and the lines will approximate the center of the bar. Protractor head allows angles to be set and measured between the base and ruler, a rudimentary level for approximating level surfaces is incorporated in the protractor and also the 45° holder. By moving and setting the head, it can be used as a gauge or to transfer dimensions. Marking the work surface, with the included Scribe Point stored in a hole in the Square Base. It is used to find the center of the round jobs, in woodworking, the starting raw material is neither flat nor square, however, the end product such as a table must be flat and have corners and legs which are square. In metalworking, it is useful for a variety of layout. When used correctly, a high degree of precision can be achieved. One use would be setting large items at the angle in machine vices
31.
Hip roof
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A hip roof, hip-roof or hipped roof, is a type of roof where all sides slope downwards to the walls, usually with a fairly gentle slope. Thus a hipped roof house has no gables or other vertical sides to the roof, a square hip roof is shaped like a pyramid. Hip roofs on houses could have two sides and two trapezoidal ones. A hip roof on a plan has four faces. They are almost always at the pitch or slope, which makes them symmetrical about the centerlines. Hip roofs often have a consistent level fascia, meaning that a gutter can be fitted all around, Hip roofs often have dormer slanted sides. Hip roofs are more difficult to construct than a gabled roof, Hip roofs can be constructed on a wide variety of plan shapes. Each ridge is central over the rectangle of the building below it, the triangular faces of the roof are called the hip ends, and they are bounded by the hips themselves. The hips and hip rafters sit on a corner of the building. Where the building has a corner, a valley makes the join between the sloping surfaces. They have the advantage of giving a compact, solid appearance to a structure, in modern domestic architecture, hip roofs are commonly seen in bungalows and cottages, and have been integral to styles such as the American Foursquare. However, the hip roof has been used in different styles of architecture. A hip roof is self-bracing, requiring less diagonal bracing than a gable roof, Hip roofs are thus much better suited for hurricane regions than gable roofs. Hip roofs have no large, flat, or slab-sided ends to catch wind and are much more stable than gable roofs. However, for a region, the roof also has to be steep-sloped. When wind flows over a shallow sloped hip roof, the roof can behave like an airplane wing, lift is then created on the leeward side. The flatter the roof, the more likely this will happen, a steeper pitched hip roof tends to cause the wind to stall as it goes over the roof, breaking up the effect. If the roof slopes are less than 35 degrees from horizontal, greater than 35 degrees, and not only does wind blowing over it encounter a stalling effect, but the roof is actually held down on the wall plate by the wind pressure
32.
Try square
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A try square is a woodworking or a metalworking tool used for marking and measuring a piece of wood. The square refers to the primary use of measuring the accuracy of a right angle. A piece of wood that is rectangular, flat, and has all edges 90 degrees is called four square, a board is often milled four square in preparation for using it in building furniture. A traditional try square has a blade made of steel that is riveted to a wooden handle or stock. The inside of the wooden stock usually has a brass strip fixed to it to reduce wear, some blades also have graduations for measurement. Modern try squares may be all-metal, with stocks that are either die-cast or extruded, try square is so called because it is used to try the squareness. Combination square Machinist square Set square Steel square Speed square
33.
Orange Judd
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Orange Judd was an American agricultural chemist, editor, and publisher. Judd was born of a family near Niagara Falls in Niagara County. His grandfather, also named Orange Judd, came from Tyringham, Massachusetts and his father, Ozias Judd, fought at Black Rock in 1813. Orange Judds mother was Rheuama Wright, daughter of David Wright who was a private in the New York Militia during the Revolution and his daughter from his first marriage, Sarah Ford, married George Brown Goode in 1877. Orange Judds brother, David Wright, was successful and kept close connections to Orange. Wright was the editor and proprietor of The Hearth and Home, one of Judds periodicals under his publishing firm Orange Judd, by 1883 Wright had become president of the company. Prior to that in 1871 he had also elected as a Republican to the New York legislature. In 1847 Judd graduated from Wesleyan University, in 1850 he began studying analytical and agricultural chemistry at Yale for the next three years with John Pitkin Norton. In 1852 he took a job lecturing on agriculture in Windham County, Judd recalled that his chemistry research at Yale lowered much of his hope for the science, deeming that much of the so-called agricultural science is yet unreliable. Judd still sought a way to bring the latest research to farmers, in 1853 he was made editor of the American Agriculturist, then run by its founders, Anthony B. Allen and his brother Richard L. Allen. He became owner and publisher in 1856, in 1856 Judd moved to Flushing, New York where he lived until 1871. Judd championed the idea of clear and concise writing in journals, editors would obtain scientific material from colleges and would evaluate it and make it accessible for their readers. His success helped make American Agriculturist into one of the leading journals in the nation, going from a circulation 1,000 in 1856. However the paper was hard hit by the depression of 1873 and he would stay there until 1881, alongside being the agricultural editor of the New York Times from 1855 to 1863. He became the member of the firm Orange Judd and Company, located in Chicago. However he was brought home due to illness where he reached almost the point of death. In 1866 he became president of the Alumni Association of Wesleyan and he again traveled to Europe in 1871 with his family through numerous countries. Around this time he began to take a greater interest in the affairs of Wesleyan University and he edited their first edition of the Alumni Record
34.
International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
35.
Fine Woodworking
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Fine Woodworking is a woodworking magazine published by Taunton Press in Newtown, Connecticut, USA. The magazine began publication in 1975, with simple monochrome printing, the magazine focuses on the very best of woodworking techniques at the highest level of skill. Articles include practical tutorials on technique, the theory of timber, finishes or tools, the magazine emphasizes high-quality work regardless of the difficulty of execution. Tage Frid R. Bruce Hoadley Richard Raffan Since the first issues, Taunton encourages this, with sales of back issues and the publication of indexes. Collected volumes have also produced in book form. These began as collections of the best general articles in a numbered series Fine Woodworking Techniques, later there were more strongly-themed Best of Fine Woodworking collections on particular topics such as, Joinery, Making and Modifying Machines, Bending Wood, Woodshop Specialities and many others. Taunton also operates a website for Fine Woodworking
36.
Measuring instrument
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A measuring instrument is a device for measuring a physical quantity. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of objects and events. Established standard objects and events are used as units, and the process of measurement gives a number relating the item under study, measuring instruments, and formal test methods which define the instruments use, are the means by which these relations of numbers are obtained. All measuring instruments are subject to varying degrees of instrument error, scientists, engineers and other humans use a vast range of instruments to perform their measurements. These instruments may range from simple objects such as rulers and stopwatches to electron microscopes, virtual instrumentation is widely used in the development of modern measuring instruments. In the past, a common time measuring instrument was the sundial, today, the usual measuring instruments for time are clocks and watches. For highly accurate measurement of time a clock is used. Stop watches are used to measure time in some sports. Energy is measured by an energy meter, examples of energy meters include, An electricity meter measures energy directly in kilowatt hours. A gas meter measures energy indirectly by recording the volume of gas used and this figure can then be converted to a measure of energy by multiplying it by the calorific value of the gas. A physical system that exchanges energy may be described by the amount of energy exchanged per time-interval, for the ranges of power-values see, Orders of magnitude. Action describes energy summed up over the time a process lasts and its dimension is the same as that of an angular momentum. A phototube provides a measurement which permits the calculation of the quantized action of light. This includes basic quantities found in classical- and continuum mechanics, dumpy level Laser line level Spirit level Gyroscope Ballistic pendulum, indirectly by calculation and or gauging Considerations related to electric charge dominate electricity and electronics. Electrical charges interact via a field and that field is called electric if the charge doesnt move. If the charge moves, thus realizing an electric current, especially in a neutral conductor. Electricity can be given a quality — a potential, and electricity has a substance-like property, the electric charge. Energy in elementary electrodynamics is calculated by multiplying the potential by the amount of charge found at that potential, potential times charge, electrometer is often used to reconfirm the phenomenon of contact electricity leading to triboelectric sequences
37.
Scale ruler
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An architects scale is a specialized ruler designed to facilitate the drafting and measuring of architectural drawings, such as floor plans and orthographic projections. Because the scale of such drawings are often smaller than life-size, for accuracy and longevity, the material used should be dimensionally stable and durable. Scales were traditionally made of wood, but today they are made of rigid plastic or aluminium. Architects scales may be flat, with 4 scales, or have a symmetric 3-lobed cross-section, in the United States, and prior to metrification in Britain, Canada and Australia, architects scales are/were marked as a ratio of x inches-to-the-foot. It is not to be confused with a true unitless ratio -- a 1,5 architectural scale would be a 1,60 unitless scale, therefore, a drawing will indicate both its scale and the unit of measurement being used. In Britain, and elsewhere, the units used on architectural drawings are the units millimetres and metres. In Britain, for rulers, the paired scales often found on architects scales are, For triangular rulers
38.
Beam compass
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A beam compass is a compass with a beam and sliding sockets or cursors for drawing and dividing circles larger than those made by a regular pair of compasses. The instrument can be as a whole, or made on the spot with individual sockets, a draftsmans beam compass consists of a set of points and holders, mounted on a plated brass, aluminum, or electrum rod. One end is generally locked down at the end of the rod, the locked tip holder consists of a needle, for the center of the radius, and the other holds either a lead clutch, or an inking nib. There are older variants which use a wooden beam, another similar type is a Machinist or Engineers beam compass, which uses scribing points only, similar to ones used by woodworkers, except that its fine adjustment is generally more refined. These beam compasses can be extended by adding press-in rods, or by using a lockable rod connector, trammels or trammel points are the sockets or cursors that, together with the beam, make up a beam compass. Their relatively small size makes them easy to store or transport and they consist of two separate metal pieces that are usually connected by a piece of wood, The wood timber is not included in the purchase of the trammel points. It can be ripped on a table saw, a lumber yard or woodworking store should have a piece readily available to fit the opening also, metal, or pipe. They work like a scratch awl, as for any compass, there are two uses. The beam compass is used to scribe a circle, either by drawing with lead, penning by ink, the radius can be adjusted by sliding the metal point holder across a wood beam or metal rod, and locking it by turning a knob at the desired location. Some have a fine radius adjustment, the threaded adjustment is similar to that of a Screw. The only limitation is the rigidity of the beam or metal rod being used. Longer wooden beams tend to sag depending on the species of wood used, metal rods can be used as an alternative, but they also have length limitations. Some trammel sets include a support roller for attachment at mid span of the beam or rod, trammel points score a precise line by using a sharpened point, or draw a line using a lead clutch, or an ink nib. When the circular knob is turned, it micro adjusts the radius of the circle, on some, a spring and screw mechanism locks the compass at the precise desired location. Turning clockwise decreases the radius while turning increases the radius slightly. A beam compass can also be used to make a series of measurements in a precise manner. Each point is rotated 180° along a line or large circle. The indentation created by the point of the trammel is easily seen
39.
Calipers
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A caliper is a device used to measure the distance between two opposite sides of an object. A caliper can be as simple as a compass with inward or outward-facing points. The tips of the caliper are adjusted to fit across the points to be measured, the caliper is then removed and it is used in many fields such as mechanical engineering, metalworking, forestry, woodworking, science and medicine. A plurale tantum sense of the word calipers coexists in natural usage with the regular noun sense of caliper, also existing colloquially but not in formal usage is referring to a vernier caliper as a vernier or a pair of verniers. In imprecise colloquial usage, some extend this even to dial calipers. In machine-shop usage, the caliper is often used in contradistinction to micrometer. In this usage, caliper implies only the factor of the vernier or dial caliper. The earliest caliper has been found in the Greek Giglio wreck near the Italian coast, the ship find dates to the 6th century BC. The wooden piece already featured a fixed and a movable jaw, although rare finds, caliper remained in use by the Greeks and Romans. A bronze caliper, dating from 9 AD, was used for minute measurements during the Chinese Xin dynasty, the caliper had an inscription stating that it was made on a gui-you day at new moon of the first month of the first year of the Shijian guo period. The calipers included a slot and pin and graduated in inches, the modern vernier caliper, reading to thousandths of an inch, was invented by American Joseph R. Brown in 1851. It was the first practical tool for exact measurements that could be sold at a price within the reach of ordinary machinists, the inside calipers are used to measure the internal size of an object. The upper caliper in the image requires manual adjustment prior to fitting, fine setting of this caliper type is performed by tapping the caliper legs lightly on a handy surface until they will almost pass over the object. A light push against the resistance of the pivot screw then spreads the legs to the correct dimension and provides the required. The lower caliper in the image has a screw that permits it to be carefully adjusted without removal of the tool from the workpiece. Outside calipers are used to measure the size of an object. The same observations and technique apply to this type of caliper, with some understanding of their limitations and usage, these instruments can provide a high degree of accuracy and repeatability. They are especially useful when measuring over very large distances, consider if the calipers are used to measure a large diameter pipe, a vernier caliper does not have the depth capacity to straddle this large diameter while at the same time reach the outermost points of the pipes diameter
40.
Chalk line
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A chalk line or chalk box is a tool for marking long, straight lines on relatively flat surfaces, much farther than is practical by hand or with a straightedge. A chalk line draws straight lines by the action of a nylon or similar string that has been previously coated with a loose dye. The string is then laid across the surface to be marked and pulled tight, next, the string is then plucked or snapped sharply, causing the string to strike the surface, which then transfers its chalk to the surface along that straight line where it struck. Chalk lines are used to mark relatively flat surfaces. However, as long as the line is taut and the two ends of the line are in nearly the same plane, the chalk line will mark all points that the string touches on or near that plane once snapped. The objects to be marked do not need to be continuous along the line, Chalk lines can also be used across irregular surfaces and surfaces with holes in them, for example on an unfinished stud wall. The primary problems associated with maintenance of a chalk line are string breakage due to excessive tension on the line. Chalk lines and plumb-bobs are often sold as a single tool, Chalk lines have been in use since ancient Egypt, and used continuously by builders in various cultures since. Continuing development of simple but effective tool focuses on the coloration for the chalk or marking compound, as well as the outer case. In East Asia, an ink line is used in preference to a chalk line and this is a silken cord, stored on a combined reel and inkpot called a sumitsubo in Japanese. Alongside the line reel is a cavity filled with ink-soaked cotton fibres and these sumitsubo are highly decorated and much-prized by their owners. As with many tools, theyre often made by their users while apprentices. On the completion of a building, such as a temple. As part of event, a set of symbolic carpenters tools are freshly made. A sumitsubo is a tool included with them. Measuring tape Chalk line – One person operation Chalk line – Two-person operation Hand-made chalk-line
41.
Compass (drawing tool)
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A pair of compasses, also known simply as a compass, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, they can also be used as tools to measure distances, Compasses can be used for mathematics, drafting, navigation and other purposes. Compasses are usually made of metal or plastic, and consist of two connected by a hinge which can be adjusted to allow the changing of the radius of the circle drawn. Typically one part has a spike at its end, and the part a pencil. Prior to computerization, compasses and other tools for manual drafting were often packaged as a bow set with interchangeable parts, today these facilities are more often provided by computer-aided design programs, so the physical tools serve mainly a didactic purpose in teaching geometry, technical drawing, etc. Compasses are usually made of metal or plastic, and consist of two connected by a hinge which can be adjusted to allow the changing of the radius of the circle drawn. Typically one part has a spike at its end, and the part a pencil. The handle is usually half a inch long. Users can grip it between their pointer finger and thumb, there are two types of legs in a pair of compasses, the straight or the steady leg and the adjustable one. Each has a purpose, the steady leg serves as the basis or support for the needle point. The screw on your hinge holds the two legs in its position, the hinge can be adjusted depending on desired stiffness, the tighter the screw the better the compass’ performance. The needle point is located on the leg, and serves as the center point of circles that are drawn. The pencil lead draws the circle on a paper or material. This holds the lead or pen in place. Circles can be made by fastening one leg of the compasses into the paper with the spike, putting the pencil on the paper, the radius of the circle can be adjusted by changing the angle of the hinge. Distances can be measured on a map using compasses with two spikes, also called a dividing compass, to use a pair of compasses, place the points on a ruler and open it to the measurement of ½ of the measurement of the circle that is desired. For instance, if one desires to draw a 3 inch circle, next, place the point on the spot that you wish the center of your circle to be, and then rotate the section that has the pencil lead around the point, using the handle. Compasses-and-straightedge constructions are used to illustrate principles of plane geometry, although a real pair of compasses is used to draft visible illustrations, the ideal compass used in proofs is an abstract creator of perfect circles
42.
Coordinate-measuring machine
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A coordinate measuring machine is a device for measuring the physical geometrical characteristics of an object. This machine may be controlled by an operator or it may be computer controlled. Measurements are defined by an attached to the third moving axis of this machine. Probes may be mechanical, optical, laser, or white light, a machine which takes readings in six degrees of freedom and displays these readings in mathematical form is known as a CMM. The typical 3D bridge CMM is composed of three axes, X, Y and Z and these axes are orthogonal to each other in a typical three-dimensional coordinate system. Each axis has a system that indicates the location of that axis. The machine reads the input from the probe, as directed by the operator or programmer. By precisely recording the X, Y, and Z coordinates of the target and these points are collected by using a probe that is positioned manually by an operator or automatically via Direct Computer Control. The material used to construct the frame has varied over the years. Granite and steel were used in the early CMMs, today all the major CMM manufacturers build frames from aluminium alloy or some derivative and also use ceramic to increase the stiffness of the Z axis for scanning applications. Few CMM builders today still manufacture granite frame CMM due to market requirement for improved metrology dynamics, typically only low volume CMM builders and domestic manufacturers in China and India are still manufacturing granite CMM due to low technology approach and easy entry to become a CMM frame builder. The increasing trend towards scanning also requires the CMM Z axis to be stiffer and new materials have been introduced such as ceramic, Probing system Data collection and reduction system - typically includes a machine controller, desktop computer and application software. These machines can be free-standing, handheld and portable, the first 3-axis models began appearing in the 1960s and computer control debuted in the early 1970s. Leitz Germany subsequently produced a fixed machine structure with moving table, in modern machines, the gantry type superstructure has two legs and is often called a bridge. This moves freely along the table with one leg following a guide rail attached to one side of the granite table. The opposite leg simply rests on the table following the vertical surface contour. Air bearings are the method for ensuring friction free travel. In these, compressed air is forced through a series of small holes in a flat bearing surface to provide a smooth
43.
Drafting machine
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A drafting machine is a tool used in technical drawing, consisting of a pair of scales mounted to form a right angle on an articulated protractor head that allows an angular rotation. The protractor head is able to move freely across the surface of the drawing board and these guides, which act separately, ensure the movement of the set in the horizontal or vertical direction of the drawing board, and can be locked independently of each other. The drafting machine was invented by Charles H, little in 1901, and he founded the Universal Drafting Machine Company in Cleveland, Ohio, to manufacture and sell the instrument. Drafting machines were present in the offices of European companies since the 1920s. In the older sets, the movement of the protractor head was assured by a pantograph system that could keep the head in the same angular position throughout its range of motion. The arms were balanced by a system of counterweights or springs, typically, the machine is mounted on a drawing board with a hard and smooth surface, anchored to a base that allows its tilting and lifting. Thus, the realization of a drawing can be achieved in the most convenient way on a surface that can be tilted at any angle from horizontal to vertical. There are special versions for A0 double-sized boards, to make drawings, or copying-boards with background illumination
44.
Flat spline
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Before computers were used for creating engineering designs, drafting tools were employed by designers drawing by hand. To draw curves, especially for shipbuilding, draftsmen often used long, thin, flexible strips of wood, plastic, the splines were held in place with lead weights. Splines are more recently referred to as flexible curves and perform much of the original function, the main difference between splines and flexible curves is that the control points of flexible curves are entirely internal in their housing. One can recreate an original draftsmans spline device with weights and a length of thin plastic or rubber tubing. The weights are attached to the tube, the tubing is then placed over drawing paper. Crosses are marked on the paper to designate the knots or control points, the tube is then adjusted so that it passes over the control points. In 1946, mathematicians started studying the shape and derived the piecewise polynomial formula known as the spline curve. This has led to the use of such functions in computer-aided design. I. J. Schoenberg gave the spline function its name after its resemblance to the mechanical spline used by draftsmen, the origins of the spline in wood-working may show in the conjectured etymology, which connects the word spline to the word splinter. Later craftsmen have made out of rubber, steel. Spline devices help bend the wood for pianos, violins, violas, the Wright brothers used one to shape the wings of their aircraft. Lesbian rule French curve Technical drawing tools