Mathematics includes the study of such topics as quantity, structure and change. Mathematicians use patterns to formulate new conjectures; when mathematical structures are good models of real phenomena mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back; the research required to solve mathematical problems can take years or centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.
Mathematics is essential in many fields, including natural science, medicine and the social sciences. Applied mathematics has led to new mathematical disciplines, such as statistics and game theory. Mathematicians engage in pure mathematics without having any application in mind, but practical applications for what began as pure mathematics are discovered later; the history of mathematics can be seen as an ever-increasing series of abstractions. The first abstraction, shared by many animals, was that of numbers: the realization that a collection of two apples and a collection of two oranges have something in common, namely quantity of their members; as evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have recognized how to count abstract quantities, like time – days, years. Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic and geometry for taxation and other financial calculations, for building and construction, for astronomy.
The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry, it is in Babylonian mathematics that elementary arithmetic first appear in the archaeological record. The Babylonians possessed a place-value system, used a sexagesimal numeral system, still in use today for measuring angles and time. Beginning in the 6th century BC with the Pythagoreans, the Ancient Greeks began a systematic study of mathematics as a subject in its own right with Greek mathematics. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom and proof, his textbook Elements is considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is held to be Archimedes of Syracuse, he developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
Other notable achievements of Greek mathematics are conic sections, trigonometry (Hipparchus of Nicaea, the beginnings of algebra. The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics. Other notable developments of Indian mathematics include the modern definition of sine and cosine, an early form of infinite series. During the Golden Age of Islam during the 9th and 10th centuries, mathematics saw many important innovations building on Greek mathematics; the most notable achievement of Islamic mathematics was the development of algebra. Other notable achievements of the Islamic period are advances in spherical trigonometry and the addition of the decimal point to the Arabic numeral system. Many notable mathematicians from this period were Persian, such as Al-Khwarismi, Omar Khayyam and Sharaf al-Dīn al-Ṭūsī. During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.
The development of calculus by Newton and Leibniz in the 17th century revolutionized mathematics. Leonhard Euler was the most notable mathematician of the 18th century, contributing numerous theorems and discoveries; the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, differential geometry, matrix theory, number theory, statistics. In the early 20th century, Kurt Gödel transformed mathematics by publishing his incompleteness theorems, which show that any axiomatic system, consistent will contain unprovable propositions. Mathematics has since been extended, there has been a fruitful interaction between mathematics and science, to
Computer-aided design is the use of computers to aid in the creation, analysis, or optimization of a design. CAD software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, to create a database for manufacturing. CAD output is in the form of electronic files for print, machining, or other manufacturing operations; the term CADD is used. Its use in designing electronic systems is known as electronic design automation. In mechanical design it is known as mechanical design automation or computer-aided drafting, which includes the process of creating a technical drawing with the use of computer software. CAD software for mechanical design uses either vector-based graphics to depict the objects of traditional drafting, or may produce raster graphics showing the overall appearance of designed objects. However, it involves more than just shapes; as in the manual drafting of technical and engineering drawings, the output of CAD must convey information, such as materials, processes and tolerances, according to application-specific conventions.
CAD may be used to design figures in two-dimensional space. CAD is an important industrial art extensively used in many applications, including automotive and aerospace industries and architectural design and many more. CAD is widely used to produce computer animation for special effects in movies and technical manuals called DCC digital content creation; the modern ubiquity and power of computers means that perfume bottles and shampoo dispensers are designed using techniques unheard of by engineers of the 1960s. Because of its enormous economic importance, CAD has been a major driving force for research in computational geometry, computer graphics, discrete differential geometry; the design of geometric models for object shapes, in particular, is called computer-aided geometric design. Starting around the mid 1960s, with the IBM Drafting System, computer-aided design systems began to provide more capability than just an ability to reproduce manual drafting with electronic drafting, the cost-benefit for companies to switch to CAD became apparent.
The benefits of CAD systems over manual drafting are the capabilities one takes for granted from computer systems today. CAD provided the designer with the ability to perform engineering calculations. During this transition, calculations were still performed either by hand or by those individuals who could run computer programs. CAD was a revolutionary change in the engineering industry, where draftsmen and engineering roles begin to merge, it did not eliminate departments, as much as it merged departments and empowered draftsman and engineers. CAD is an example of the pervasive effect. Current computer-aided design software packages range from 2D vector-based drafting systems to 3D solid and surface modelers. Modern CAD packages can frequently allow rotations in three dimensions, allowing viewing of a designed object from any desired angle from the inside looking out; some CAD software is capable of dynamic mathematical modeling. CAD technology is used in the design of tools and machinery and in the drafting and design of all types of buildings, from small residential types to the largest commercial and industrial structures.
CAD is used for detailed engineering of 3D models or 2D drawings of physical components, but it is used throughout the engineering process from conceptual design and layout of products, through strength and dynamic analysis of assemblies to definition of manufacturing methods of components. It can be used to design objects such as jewelry, appliances, etc. Furthermore, many CAD applications now offer advanced rendering and animation capabilities so engineers can better visualize their product designs. 4D BIM is a type of virtual construction engineering simulation incorporating time or schedule related information for project management. CAD has become an important technology within the scope of computer-aided technologies, with benefits such as lower product development costs and a shortened design cycle. CAD enables designers to layout and develop work on screen, print it out and save it for future editing, saving time on their drawings. Computer-aided design is one of the many tools used by engineers and designers and is used in many ways depending on the profession of the user and the type of software in question.
CAD is one part of the whole digital product development activity within the product lifecycle management processes, as such is used together with other tools, which are either integrated modules or stand-alone products, such as: Computer-aided engineering and finite element analysis Computer-aided manufacturing including instructions to computer numerical control machines Photorealistic rendering and motion simulation. Document management and revision control using product data management. CAD is used for the accurate creation of photo simulations that are required in the preparation of environmental impact reports, in which computer-aided designs of intended buildings are superimposed into photographs of existing environments to represent what that locale will be like, where the proposed facilities are allowed to be built. Pote
Paper is a thin material produced by pressing together moist fibres of cellulose pulp derived from wood, rags or grasses, drying them into flexible sheets. It is a versatile material with many uses, including writing, packaging, decorating, a number of industrial and construction processes. Papers are essential in non-legal documentation; the pulp papermaking process is said to have been developed in China during the early 2nd century CE as early as the year 105 CE, by the Han court eunuch Cai Lun, although the earliest archaeological fragments of paper derive from the 2nd century BCE in China. The modern pulp and paper industry is global, with China leading its production and the United States right behind it; the oldest known archaeological fragments of the immediate precursor to modern paper date to the 2nd century BCE in China. The pulp paper-making process is ascribed to a 2nd-century CE Han court eunuch. In the 13th century, the knowledge and uses of paper spread from China through the Middle East to medieval Europe, where the first water powered paper mills were built.
Because paper was introduced to the West through the city of Baghdad, it was first called bagdatikos. In the 19th century, industrialization reduced the cost of manufacturing paper. In 1844, the Canadian inventor Charles Fenerty and the German F. G. Keller independently developed processes for pulping wood fibres. Before the industrialisation of paper production the most common fibre source was recycled fibres from used textiles, called rags; the rags were from hemp and cotton. A process for removing printing inks from recycled paper was invented by German jurist Justus Claproth in 1774. Today this method is called deinking, it was not until the introduction of wood pulp in 1843 that paper production was not dependent on recycled materials from ragpickers. The word "paper" is etymologically derived from Latin papyrus, which comes from the Greek πάπυρος, the word for the Cyperus papyrus plant. Papyrus is a thick, paper-like material produced from the pith of the Cyperus papyrus plant, used in ancient Egypt and other Mediterranean cultures for writing before the introduction of paper into the Middle East and Europe.
Although the word paper is etymologically derived from papyrus, the two are produced differently and the development of the first is distinct from the development of the second. Papyrus is a lamination of natural plant fibres, while paper is manufactured from fibres whose properties have been changed by maceration. To make pulp from wood, a chemical pulping process separates lignin from cellulose fibres; this is accomplished by dissolving lignin in a cooking liquor, so that it may be washed from the cellulose. Paper made from chemical pulps are known as wood-free papers–not to be confused with tree-free paper; the pulp can be bleached to produce white paper, but this consumes 5% of the fibres. There are three main chemical pulping processes: the sulfite process dates back to the 1840s and it was the dominant method extent before the second world war; the kraft process, invented in the 1870s and first used in the 1890s, is now the most practiced strategy, one of its advantages is the chemical reaction with lignin, that produces heat, which can be used to run a generator.
Most pulping operations using the kraft process are net contributors to the electricity grid or use the electricity to run an adjacent paper mill. Another advantage is that this process reuses all inorganic chemical reagents. Soda pulping is another specialty process used to pulp straws and hardwoods with high silicate content. There are two major mechanical pulps: groundwood pulp. In the TMP process, wood is chipped and fed into steam heated refiners, where the chips are squeezed and converted to fibres between two steel discs. In the groundwood process, debarked logs are fed into grinders where they are pressed against rotating stones to be made into fibres. Mechanical pulping does not remove the lignin, so the yield is high, >95%, however it causes the paper thus produced to turn yellow and become brittle over time. Mechanical pulps have rather short fibres. Although large amounts of electrical energy are required to produce mechanical pulp, it costs less than the chemical kind. Paper recycling processes can use mechanically produced pulp.
Most recycled paper contains a proportion of virgin fibre for the sake of quality. There are three main classifications of recycled fibre:. Mill broke or internal mill waste – This incorporates any substandard or grade-change paper made within the paper mill itself, which goes back into the manufacturing system to be re-pulped back into paper; such out-of-specification paper is not sold and is therefore not classified as genuine reclaimed recycled fibre, however most paper mills have been reusing their own waste fibre for many years, long before recycling became popular. Preconsumer waste – This is offcut and processing waste, such as guillotine trims and envelope blank waste.
Geometry is a branch of mathematics concerned with questions of shape, relative position of figures, the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a practical way for dealing with lengths and volumes. Geometry began to see elements of formal mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment, Euclid's Elements, set a standard for many centuries to follow. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC. Islamic scientists expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as René Descartes and Pierre de Fermat. Since and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, describing spaces that lie beyond the normal range of human experience.
While geometry has evolved throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, planes, surfaces and curves, as well as the more advanced notions of manifolds and topology or metric. Geometry has applications to many fields, including art, physics, as well as to other branches of mathematics. Contemporary geometry has many subfields: Euclidean geometry is geometry in its classical sense; the mandatory educational curriculum of the majority of nations includes the study of points, planes, triangles, similarity, solid figures and analytic geometry. Euclidean geometry has applications in computer science and various branches of modern mathematics. Differential geometry uses techniques of linear algebra to study problems in geometry, it has applications in physics, including in general relativity. Topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this means dealing with large-scale properties of spaces, such as connectedness and compactness.
Convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues using techniques of real analysis. It has close connections to convex analysis and functional analysis and important applications in number theory. Algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques, it has applications including cryptography and string theory. Discrete geometry is concerned with questions of relative position of simple geometric objects, such as points and circles, it shares many principles with combinatorics. Computational geometry deals with algorithms and their implementations for manipulating geometrical objects. Although being a young area of geometry, it has many applications in computer vision, image processing, computer-aided design, medical imaging, etc; the earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles and volumes, which were developed to meet some practical need in surveying, construction and various crafts.
The earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, or frustum. Clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiter's position and motion within time-velocity space; these geometric procedures anticipated the Oxford Calculators, including the mean speed theorem, by 14 centuries. South of Egypt the ancient Nubians established a system of geometry including early versions of sun clocks. In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. Pythagoras established the Pythagorean School, credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history.
Eudoxus developed the method of exhaustion, which allowed the calculation of areas and volumes of curvilinear figures, as well as a theory of ratios that avoided the problem of incommensurable magnitudes, which enabled subsequent geometers to make significant advances. Around 300 BC, geometry was revolutionized by Euclid, whose Elements considered the most successful and influential textbook of all time, introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom and proof. Although most of the contents of the Elements were known, Euclid arranged them into a single, coherent logical framework; the Elements was known to all educated people in the West until the middle of the 20th century and its contents are still taught in geometry classes today. Archimedes of Syracuse used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, gave remarkably accurate approximations of Pi.
He studied the sp
Plastic is material consisting of any of a wide range of synthetic or semi-synthetic organic compounds that are malleable and so can be molded into solid objects. Plasticity is the general property of all materials which can deform irreversibly without breaking but, in the class of moldable polymers, this occurs to such a degree that their actual name derives from this specific ability. Plastics are organic polymers of high molecular mass and contain other substances, they are synthetic, most derived from petrochemicals, however, an array of variants are made from renewable materials such as polylactic acid from corn or cellulosics from cotton linters. Due to their low cost, ease of manufacture and imperviousness to water, plastics are used in a multitude of products of different scale, including paper clips and spacecraft, they have prevailed over traditional materials, such as wood, stone and bone, metal and ceramic, in some products left to natural materials. In developed economies, about a third of plastic is used in packaging and the same in buildings in applications such as piping, plumbing or vinyl siding.
Other uses include automobiles and toys. In the developing world, the applications of plastic may differ—42% of India's consumption is used in packaging. Plastics have many uses in the medical field as well, with the introduction of polymer implants and other medical devices derived at least from plastic; the field of plastic surgery is not named for use of plastic materials, but rather the meaning of the word plasticity, with regard to the reshaping of flesh. The world's first synthetic plastic was bakelite, invented in New York in 1907 by Leo Baekeland who coined the term'plastics'. Many chemists have contributed to the materials science of plastics, including Nobel laureate Hermann Staudinger, called "the father of polymer chemistry" and Herman Mark, known as "the father of polymer physics"; the success and dominance of plastics starting in the early 20th century led to environmental concerns regarding its slow decomposition rate after being discarded as trash due to its composition of large molecules.
Toward the end of the century, one approach to this problem was met with wide efforts toward recycling. The word plastic derives from the Greek πλαστικός meaning "capable of being shaped or molded" and, in turn, from πλαστός meaning "molded"; the plasticity, or malleability, of the material during manufacture allows it to be cast, pressed, or extruded into a variety of shapes, such as: films, plates, bottles, amongst many others. The common noun plastic should not be confused with the technical adjective plastic; the adjective is applicable to any material which undergoes a plastic deformation, or permanent change of shape, when strained beyond a certain point. For example, aluminum, stamped or forged exhibits plasticity in this sense, but is not plastic in the common sense. By contrast, some plastics will, in their finished forms, break before deforming and therefore are not plastic in the technical sense. Most plastics contain organic polymers; the vast majority of these polymers are formed from chains of carbon atoms,'pure' or with the addition of: oxygen, nitrogen, or sulfur.
The chains comprise many repeat units, formed from monomers. Each polymer chain will have several thousand repeating units; the backbone is the part of the chain, on the "main path", linking together a large number of repeat units. To customize the properties of a plastic, different molecular groups "hang" from this backbone; these pendant units are "hung" on the monomers, before the monomers themselves are linked together to form the polymer chain. It is the structure of these side chains; the molecular structure of the repeating unit can be fine tuned to influence specific properties in the polymer. Plastics are classified by: the chemical structure of the polymer's backbone and side chains. Plastics can be classified by: the chemical process used in their synthesis, such as: condensation and cross-linking. Plastics can be classified by: their various physical properties, such as: hardness, tensile strength, resistance to heat and glass transition temperature, by their chemical properties, such as the organic chemistry of the polymer and its resistance and reaction to various chemical products and processes, such as: organic solvents and ionizing radiation.
In particular, most plastics will melt upon heating to a few hundred degrees celsius. Other classifications are based on qualities that are relevant for product design. Examples of such qualities and classes are: thermoplastics and thermosets, conductive polymers, biodegradable plastics and engineering plastics and other plastics with particular structures, such as elastomers. One important classification of plastics is by the permanence or impermanence of their form, or whether they are: thermoplastics or thermosetting polymers. Thermoplastics are the plastics that, when heated, do not undergo chemical change in their composition and so can be molded again and again. Examples include: polyethylene, polypropylene and polyvinyl chloride. Common thermoplastics range from 20,000 to 500,000 amu, while thermosets are assumed to have infinite molecular weight. Thermosets, or thermosetting polymers, can melt and take shape only once: after they have solidified, they stay solid. In the thermosetting process, a chemical reaction occurs, irreversible.
A technical pen is a specialized instrument used by an engineer, architect, or drafter to make lines of constant width for architectural, engineering, or technical drawings. "Rapidograph" is a trademarked name for one type of technical pen. Technical pens use either a replaceable ink cartridge. Early technical pens consisted of a small pair of calipers, having one flat and one bowed leg holding ink between them. By adjusting the gap between the legs the width of the line drawn by the pen could be adjusted; such pens, kept at a constant angle to the paper, were used for ruling lines, but not for cursive handwriting, nor for off-hand flourishes. The Graphos technical pen introduced in 1934 miniaturized the caliper principle and made the points interchangeable; the Sheaffer company produced an expensive drafting set which included such pens for use on linen prints. These sets were presented to a draftsperson upon completing'time served', which marked the end of the apprenticeship. In the 1950s, fountain pens with cylindrical points became available, but they were complex instruments with tubes holding a tiny shaft.
To release ink the shaft is depressed and a line of about the width of the exterior diameter of the tube can be drawn. Additionally, in models, the tube had a small ledge that narrowed its end, that—while maintaining the line thickness—made the tube thicker along most of its length and protected ink from spilling while drawing along the edge of a rule, set-square, T-square or other template; some special, more expensive nibs were equipped with tubes made of tungsten carbide or with their tips made of synthetic precious stones such as sapphire, to slow their wear on hard surfaces. In the 1960s, the pen's design evolved to feature tubes of ink that were filled with a Pasteur pipette or from a narrow spout on a special bottle of ink; such pens came in sets of various sizes, several pen points which were installed into the holders that contained a filled fountain, which in turn would be screwed into a handle. The construction and number of parts varied depending on the company, the parts were not cross-compatible in most cases.
Some designs had specially designed channels to allow better air flow in between the wall of the external grip and the point assembly. This made ink flow more reliable; the general drawback of this group of pens is that they have to be and cleaned to remove all ink from the tubing, otherwise it would set and could not be removed. In the United States, several firms produced this kind of technical pen: WRICO, Koh-I-Noor; each had its own proprietary sequence of line widths, meaning that the widths were not standardized across the industry, each company's specifications for the widths did not match the others. And the specifications were given as fractions of an inch instead of fractions of a millimeter. In the case of technical pens made for the US market, they were marked with both proprietary symbolic expressions and standard metric dimensions denominated in millimetres. For the rest of the world, the most recognized brands were Staedtler and Faber-Castell; some other brands that manufacture technical pen not following ISO standards are Faber-Castell, Alvin, Standardgraph.
A full set of pens would have the following nib sizes: 0.13, 0.18, 0.25, 0.35, 0.5, 0.7, 1.0, 1.4, 2.0 mm, which correspond to the line widths as defined in ISO 128. However, the International Organization for Standardization called for four pen widths and set a colour code for each: 0.25, 0.35, 0.5, 0.7. Text of 5 mm in height has a stroke or line thickness of 0.5 mm, so requires a brown-nibbed 0.5 mm pen. If this text were used in an ISO-sized document, the document were reproduced at half its original size, the text would be rendered 3.5 mm high with a stroke thickness of 0.35 mm—the yellow-nib size. Thus, changes to reductions or enlargements can be made as everything is in proportion; this worldwide standard ensures that drawings can always be legible after microfilming and faxing. The main drafting sets of four nibs came in two kinds: Silver; the Silver was for rough tracing paper, the Gold was for plastic film. Drawing boards changed as a result of technical pens—a hard surface was required, when plastic film was used, the static attraction between plastic cursors, T-squares, set-squares etc. meant that as one lifted the edge from the film, the film would rise through static attraction and the ink would blot.
The solution was to stick down a plastic sheet that attracted the film more than the drafting instruments. The tracing paper or velograph sheet would be placed on the Ozalid sheet stuck onto the drawing board and the air brushed away. Brushing charged the surface, the film would be taped taut; when pen plotters became widespread, a special variety of point assemblies was produced. These had the basic characteristics of the standard pen nib, but the tube was much thicker to strengthen it against quick l
A caliper is a device used to measure the distance between two opposite sides of an object. Many types of calipers permit reading out a measurement on a ruled scale, a dial, or a digital display, but a caliper can be as simple as a compass with outward-facing points. The tips of the caliper are adjusted to fit across the points to be measured and the caliper is removed and the distance read by measuring between the tips with a measuring tool, such as a ruler, it is used in many fields such as mechanical engineering, forestry, woodworking and medicine. A plurale tantum sense of the word "calipers" coexists in natural usage with the regular noun sense of "caliper"; that is, sometimes a caliper is treated cognitively like a pair of glasses or a pair of scissors, resulting in a phrase such as "hand me those calipers" or "those calipers are mine" in reference to one unit. 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 speakers extend this to dial calipers, although they involve no vernier scale.
In machine-shop usage, the term "caliper" is used in contradistinction to "micrometer" though outside micrometers are technically a form of caliper. In this usage, "caliper" implies only the form factor of the 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 featured a fixed and a movable jaw. Although rare finds, caliper remained in use by the 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 and tenths of an inch." 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 on a handy surface until they will pass over the object. A light push against the resistance of the central pivot screw spreads the legs to the correct dimension and provides the required, consistent feel that ensures a repeatable measurement; the lower caliper in the image has an adjusting screw that permits it to be adjusted without removal of the tool from the workpiece. Outside calipers are used to measure the external size of an object; the same observations and technique apply to this type of caliper, as for the above inside caliper. With some understanding of their limitations and usage, these instruments can provide a high degree of accuracy and repeatability, they are useful when measuring over large distances. 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 pipe's diameter.
They are made from high carbon steel. In the metalworking field, a divider caliper, popularly called a compass, is used in the process of marking out locations; the points are sharpened so that they act as scribers, one leg can be placed in the dimple created by a center or prick punch and the other leg pivoted so that it scribes a line on the workpiece's surface, thus forming an arc or circle. A divider caliper is used to measure a distance between two points on a map; the two caliper's ends are brought to the two points. The caliper's opening is either measured on a separate ruler and converted to the actual distance, or it is measured directly on a scale drawn on the map. On a nautical chart the distance is measured on the latitude scale appearing on the sides of the map: one minute of arc of latitude is one nautical mile or 1852 metres. Dividers are used in the medical profession. An ECG caliper transfers distance on an electrocardiogram. A pocket caliper version was invented by cardiologist Robert A. Mackin.
Oddleg calipers, Hermaphrodite calipers, or Oddleg jennys, as pictured on the left, are used to scribe a line at a set distance from the edge of a workpiece. The bent leg is used to run along the workpiece edge while the scriber makes its mark at a predetermined distance, this ensures a line parallel to the edge. In the diagram at left, the uppermost caliper has a slight shoulder in the bent leg allowing it to sit on the edge more securely, the lower caliper lacks this feature but has a renewable scriber that can be adjusted for wear, as well as being replaced when excessively worn; the vernier and digital calipers give a direct reading of the distance measured with high accuracy and precision. They are functionally identical, with different ways of reading the result; these calipers comprise a calibrated scale with a fixed jaw, another jaw, with a pointer, that slides along the scale. The distance between the jaws is read in different ways for the three types; the simplest method is to read the position of the pointer directly on the scale.
When the pointer is between two markings, the user can mentally interpolate to improve the precision of the reading