1.
Straight edge
–
Straight edge is a subculture of hardcore punk whose adherents refrain from using alcohol, tobacco and other recreational drugs, in reaction to the excesses of punk subculture. For some, this extends to refraining from engaging in sex, following a vegetarian or vegan diet. The term straight edge was adopted from the 1981 song Straight Edge by the punk band Minor Threat. Straight edge emerged amid the early-1980s hardcore punk scene, since then, a wide variety of beliefs and ideas have been associated with some members of the movement, including vegetarianism and animal rights. Ross Haenfler writes that as of the late 1990s, approximately three out of four straight edge participants were vegetarian or vegan, disagreements often arise as to the primary reasons for living straight edge. Straight edge politics are primarily left-wing and revolutionary but there have been conservative offshoots, in 1999, William Tsitsos wrote that straight edge had gone through three eras since its founding in the early 1980s. Bent edge began as a counter-movement to straight edge by members of the Washington, D. C. hardcore scene who were frustrated by the rigidity and intolerance in the scene. During the youth crew era, which started in the mid-1980s, by the early 1990s, militant straight edge was a well-known part of the wider punk scene. In the early to mid-1990s, straight edge spread from the United States to Northern Europe, Eastern Europe, the Middle East, by the beginning of the 2000s, militant straight edge punks had largely left the broader straight edge culture and movement. While some straight edge groups are treated as a gang by law enforcement officials, Straight edge has often been approached with skepticism and hostility, despite the ideologically less dogmatic and more multifaceted character of contemporary straight edge. In the 1970s, the subculture was associated with the use of intoxicative inhalants. In 1999, William Tsitsos wrote that straight edge had gone through three eras since its founding in the early 1980s, later analysts have identified another era that has taken place since Tsitsoss writing. Straight edge grew out of punk in the late 1970s and early 1980s. Straight edge individuals of this era often associated with the original punk ideals such as individualism, disdain for work and school. Straight edge sentiments can be found in songs by the early 1980s band Minor Threat and this anti-inebriation movement had been developing in punk prior to Minor Threat, but their song Straight Edge was influential in giving the scene a name, and something of a figurehead. Minor Threat frontman Ian MacKaye is often credited with birthing the Straight edge name and movement, Straight edge sentiments can also be found in the song Keep it Clean by English punk band The Vibrators, and the 1970s Modern Lovers song Im Straight. As one of the few prominent 1970s hard rock icons to explicitly eschew alcohol and drug use, Straight edge started on the East Coast of the United States in Washington D. C. and quickly spread throughout the United States and Canada. By the 1980s, bands on the West Coast, such as Americas Hardcore, Stalag 13, Justice League, in the early stages of this subcultures history, concerts often consisted of both punk bands and straight edge bands

2.
Scale ruler
–
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

3.
Ruler
–
A ruler, sometimes called a rule or line gauge, is an instrument used in geometry, technical drawing, printing, engineering and building to measure distances or to rule straight lines. The ruler is a straightedge which may also contain calibrated lines to measure distances, rulers have long been made from different materials and in a wide range of sizes. Plastics have also used since they were invented, they can be molded with length markings instead of being scribed. Metal is used for more durable rulers for use in the workshop,12 inches or 30 cm in length is useful for a ruler to be kept on a desk to help in drawing. Shorter rulers are convenient for keeping in a pocket, longer rulers, e. g.18 inches are necessary in some cases. Rigid wooden or plastic yardsticks,1 yard long, and meter sticks,1 meter long, are also used, classically, long measuring rods were used for larger projects, now superseded by tape measure or laser rangefinders. Desk rulers are used for three purposes, to measure, to aid in drawing straight lines and as a straight guide for cutting and scoring with a blade. Practical rulers have distance markings along their edges, a line gauge is a type of ruler used in the printing industry. These may be made from a variety of materials, typically metal or clear plastic, units of measurement on a basic line gauge usually include inches, agate, picas, and points. More detailed line gauges may contain sample widths of lines, samples of common type in several point sizes, measuring instruments similar in function to rulers are made portable by folding or retracting into a coil when not in use. When extended for use, they are straight, like a ruler, the illustrations on this page show a 2-meter carpenters rule, which folds down to a length of 24 cm to easily fit in a pocket, and a 5-meter-long tape, which retracts into a small housing. A flexible length measuring instrument which is not necessarily straight in use is the tailors fabric tape measure and it is used to measure around a solid body, e. g. a persons waist measurement, as well as linear measurement, e. g. inside leg. It is rolled up when not in use, taking up little space, a contraction rule is made having larger divisions than standard measures to allow for shrinkage of a metal casting. They may also be known as a shrinkage or shrink rule, a ruler software program can be used to measure pixels on a computer screen or mobile phone. These programs are known as screen rulers. In geometry, a ruler without any marks on it may be used only for drawing lines between points. A straightedge is used to help draw accurate graphs and tables. A ruler and compass construction refers to using an unmarked ruler

4.
Laser line level
–
A laser line level is a tool combining a spirit level and/or plumb bob with a laser to display an accurately horizontal or vertical illuminated line on a surface the laser line level is laid against. Laser line levels are used wherever accurate verticals and horizontals are required, typically in the construction, some models are inexpensive enough for do-it-yourself applications. The laser beam is fanned to produce a thin plane beam accurately horizontal or vertical, a more advanced device may be accurate to within 0.3 mm/m, while lower-end models may be closer to 1.5 mm/m. The illuminated line is necessarily absolutely straight, so that the level can be used as a straightedge, for example, to see if a shelf is warped. Dumpy level Theodolite List of laser articles Laser Machine Control Checking a level for accuracy

5.
Winding stick
–
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

6.
Compass-and-straightedge construction
–
The idealized ruler, known as a straightedge, is assumed to be infinite in length, and has no markings on it and only one edge. The compass is assumed to collapse when lifted from the page, more formally, the only permissible constructions are those granted by Euclids first three postulates. It turns out to be the case that every point constructible using straightedge, the ancient Greek mathematicians first conceived compass-and-straightedge constructions, and a number of ancient problems in plane geometry impose this restriction. The ancient Greeks developed many constructions, but in cases were unable to do so. Gauss showed that some polygons are constructible but that most are not, some of the most famous straightedge-and-compass problems were proven impossible by Pierre Wantzel in 1837, using the mathematical theory of fields. In spite of existing proofs of impossibility, some persist in trying to solve these problems, in terms of algebra, a length is constructible if and only if it represents a constructible number, and an angle is constructible if and only if its cosine is a constructible number. A number is constructible if and only if it can be using the four basic arithmetic operations. Circles can only be starting from two given points, the centre and a point on the circle. The compass may or may not collapse when its not drawing a circle, the straightedge is infinitely long, but it has no markings on it and has only one straight edge, unlike ordinary rulers. It can only be used to draw a segment between two points or to extend an existing segment. The modern compass generally does not collapse and several modern constructions use this feature and it would appear that the modern compass is a more powerful instrument than the ancient collapsing compass. However, by Proposition 2 of Book 1 of Euclids Elements, although the proposition is correct, its proofs have a long and checkered history. Eyeballing it and getting close does not count as a solution and that is, it must have a finite number of steps, and not be the limit of ever closer approximations. One of the purposes of Greek mathematics was to find exact constructions for various lengths, for example. The Greeks could not find constructions for these three problems, among others, Squaring the circle, Drawing a square the same area as a given circle, doubling the cube, Drawing a cube with twice the volume of a given cube. Trisecting the angle, Dividing a given angle into three smaller angles all of the same size, for 2000 years people tried to find constructions within the limits set above, and failed. All three have now been proven under mathematical rules to be generally impossible, the ancient Greek mathematicians first attempted compass-and-straightedge constructions, and they discovered how to construct sums, differences, products, ratios, and square roots of given lengths. They could also construct half of an angle, a square whose area is twice that of another square, a square having the same area as a given polygon

7.
Euclidean geometry
–
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry, the Elements. Euclids method consists in assuming a set of intuitively appealing axioms. Although many of Euclids results had been stated by earlier mathematicians, Euclid was the first to show how these propositions could fit into a comprehensive deductive and logical system. The Elements begins with plane geometry, still taught in school as the first axiomatic system. It goes on to the geometry of three dimensions. Much of the Elements states results of what are now called algebra and number theory, for more than two thousand years, the adjective Euclidean was unnecessary because no other sort of geometry had been conceived. Euclids axioms seemed so obvious that any theorem proved from them was deemed true in an absolute, often metaphysical. Today, however, many other self-consistent non-Euclidean geometries are known, Euclidean geometry is an example of synthetic geometry, in that it proceeds logically from axioms to propositions without the use of coordinates. This is in contrast to analytic geometry, which uses coordinates, the Elements is mainly a systematization of earlier knowledge of geometry. Its improvement over earlier treatments was recognized, with the result that there was little interest in preserving the earlier ones. There are 13 total books in the Elements, Books I–IV, Books V and VII–X deal with number theory, with numbers treated geometrically via their representation as line segments with various lengths. Notions such as numbers and rational and irrational numbers are introduced. The infinitude of prime numbers is proved, a typical result is the 1,3 ratio between the volume of a cone and a cylinder with the same height and base. Euclidean geometry is a system, in which all theorems are derived from a small number of axioms. To produce a straight line continuously in a straight line. To describe a circle with any centre and distance and that all right angles are equal to one another. Although Euclids statement of the only explicitly asserts the existence of the constructions. The Elements also include the five common notions, Things that are equal to the same thing are also equal to one another

8.
Compass (drawing tool)
–
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