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Protractor
A protractor is a measuring instrument, typically made of transparent plastic or glass, for measuring angles. Some protractors are simple half-discs or full circles. More advanced protractors, such as the bevel protractor, have one or two swinging arms, which can be used to help measure the angle. Typical Most protractors measure angles in degrees (°). Radian-scale protractors measure angles in radians. Most protractors are divided into 180 equal parts. Some precision protractors further divide degrees into arcminutes. They are used in mechanics, engineering and geometry. Bevel A bevel protractor is a graduated circular protractor with one pivoted arm; used for measuring or marking off angles. Sometimes Vernier scales are attached to give more precise readings. It has wide application in architectural and mechanical drawing, although its use is decreasing with the availability of modern drawing software or CAD. Universal bevel protractors are also used by toolmakers ...
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Protractor2
A protractor is a measuring instrument, typically made of transparent plastic or glass, for measuring angles. Some protractors are simple half-discs or full circles. More advanced protractors, such as the bevel protractor, have one or two swinging arms, which can be used to help measure the angle. Typical Most protractors measure angles in degrees (°). Radian-scale protractors measure angles in radians. Most protractors are divided into 180 equal parts. Some precision protractors further divide degrees into arcminutes. They are used in mechanics, engineering and geometry. Bevel A bevel protractor is a graduated circular protractor with one pivoted arm; used for measuring or marking off angles. Sometimes Vernier scales are attached to give more precise readings. It has wide application in architectural and mechanical drawing, although its use is decreasing with the availability of modern drawing software or CAD. Universal bevel protractors are also used by toolmakers ...
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Goniometer
A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, γωνία (''gōnía'') 'angle' and μέτρον (''métron'') ' measure'. The first known description of a goniometer, based on the astrolabe, was by Gemma Frisius in 1538. Applications Surveying Prior to the invention of the theodolite, the goniometer was used in surveying. The application of triangulation to geodesy was described in the second (1533) edition of ''Cosmograficus liber'' by Petri Appiani as a 16-page appendix by Frisius entitled ''Libellus de locorum describendorum ratione''. Communications The Bellini–Tosi direction finder was a type of radio direction finder that was widely used from World War I to World War II. It used the signals from two crossed antennas, or four individual antennas simulating two crossed ones, to re-create the radio signal in a small area between two loop ...
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Angle
In Euclidean 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 the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles. Two intersecting curves may also define an angle, which is the angle of the rays lying tangent to the respective curves at their point of intersection. ''Angle'' is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. 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. History and etymology The word ''angle'' comes from the Latin word ''angulus'', meaning "corner"; cognate words ar ...
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Dimensional Instruments
A measuring instrument is a device to measure a physical quantity. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world 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 and the referenced unit of measurement. Measuring instruments, and formal test methods which define the instrument's use, are the means by which these relations of numbers are obtained. All measuring instruments are subject to varying degrees of instrument error and measurement uncertainty. These instruments may range from simple objects such as rulers and stopwatches to electron microscopes and particle accelerators. Virtual instrumentation is widely used in the development of modern measuring instruments. Time In the past, a common time measuring instrument was the sundial. Today, the usual measuring instrum ...
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Romer
A Reference Card or "Romer" is a device for increasing the accuracy when reading a grid reference from a map. Made from transparent plastic, paper or other materials, they are also found on most baseplate compasses. Essentially, it is a specially marked-out ruler which matches the scale of the map in use. The scales are laid out in reverse, such that by lining up the numbers given in the grid reference with the gridlines for the square in question, the corner of the Romer lies on the location whose grid reference you wish to read. Some transparent versions have a small hole at the origin when this is not at the corner of the Reference Card. This allows access to the map such that the location could be marked with a pencil if using the Reference Card in reverse having been given a grid reference to start with. They are used in many types of land navigation and map reading, to give a more accurate grid reference than one just estimated by eye from the grid lines on the map. While R ...
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Centiturn
A turn is a unit of plane angle measurement equal to  radians, 360  degrees or 400 gradians. Subdivisions of a turn include half-turns, quarter-turns, centiturns, milliturns, etc. The closely related terms ''cycle'' and ''revolution'' are not equivalent to a turn. Subdivisions A turn can be divided in 100 centiturns or milliturns, with each milliturn corresponding to an angle of 0.36°, which can also be written as 21′ 36″. A protractor divided in centiturns is normally called a "percentage protractor". Binary fractions of a turn are also used. Sailors have traditionally divided a turn into 32 compass points, which implicitly have an angular separation of 1/32 turn. The ''binary degree'', also known as the '' binary radian'' (or ''brad''), is  turn. The binary degree is used in computing so that an angle can be represented to the maximum possible precision in a single byte. Other measures of angle used in computing may be based on divid ...
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Technical Drawing Tools
Drafting tools may be used for measurement and layout of drawings, or to improve the consistency and speed of creation of standard drawing elements. Tools such as pens and pencils mark the drawing medium. Other tools such as straight edges, assist the operator in drawing straight lines, or assist the operator in drawing complicated shapes repeatedly. Various scales and the protractor are used to measure the lengths of lines and angles, allowing accurate scale drawing to be carried out. The compass is used to draw arcs and circles. A drawing board was used to hold the drawing media in place; later boards included drafting machines that sped the layout of straight lines and angles. Tools such as templates and lettering guides assisted in the drawing of repetitive elements such as circles, ellipses, schematic symbols and text. Other auxiliary tools were used for special drawing purposes or for functions related to the preparation and revision of drawings. The tools used for manual ...
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Birkhoff's Axioms
In 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry in the plane, sometimes referred to as Birkhoff's axioms. These postulates are all based on basic geometry that can be confirmed experimentally with a scale and protractor. Since the postulates build upon the real numbers, the approach is similar to a model-based introduction to Euclidean geometry. Birkhoff's axiom system was utilized in the secondary-school textbook by Birkhoff and Beatley. These axioms were also modified by the School Mathematics Study Group to provide a new standard for teaching high school geometry, known aSMSG axioms A few other textbooks in the foundations of geometry use variants of Birkhoff's axioms. Postulates The distance between two points and  is denoted by , and the angle formed by three points is denoted by . Postulate I: Postulate of line measure. The set of points on any line can be put into a 1:1 correspondence with the real numbers so that for all point ...
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Measuring Instrument
A measuring instrument is a device to measure a physical quantity. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world 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 and the referenced unit of measurement. Measuring instruments, and formal test methods which define the instrument's use, are the means by which these relations of numbers are obtained. All measuring instruments are subject to varying degrees of instrument error and measurement uncertainty. These instruments may range from simple objects such as rulers and stopwatches to electron microscopes and particle accelerators. Virtual instrumentation is widely used in the development of modern measuring instruments. Time In the past, a common time measuring instrument was the sundial. Today, the usual measur ...
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Protractor Triangle
A set square or triangle (American English) is an object used in engineering and technical drawing, with the aim of providing a straightedge at a right angle or other particular planar angle to a baseline. The simplest form of set square is a triangular piece of transparent plastic (or formerly of polished wood) with the centre removed. More commonly the set square bears the markings of a ruler and a half circle protractor. The outer edges are typically bevelled. These set squares come in two usual forms, both right triangles: one with 90-45-45 degree angles, the other with 30-60-90 degree angles. Combining the two forms by placing the hypotenuses together will also yield 15° and 75° angles. They are often purchased in packs with protractors and compasses. Less commonly found is the adjustable set square. Here, the body of the object is cut in half and rejoined with a hinge marked with angles. Adjustment to the marked angle will produce any desired angle up to a maximu ...
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Mathematical Tools
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ...
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Sliding T Bevel
A sliding T bevel, also known as a bevel gauge or false square is an adjustable gauge for setting and transferring angles. Different from the square, which is fixed and can only set a 90° angle, the sliding T bevel can set any angle and transfer it on another piece. The bevel gauge is composed of two elements connected with a thumbscrew or wing nut, which allows the blade to pivot and be locked at any angle. The handle is usually made of wood or plastic and the blade of metal. The bevel can be used to duplicate an existing angle, or set to a desired angle by using it with any number of other measuring tools (such as a protractor, or framing square). See also *Bevel A bevelled edge (UK) or beveled edge (US) is an edge of a structure that is not perpendicular to the faces of the piece. The words bevel and chamfer overlap in usage; in general usage they are often interchanged, while in technical usage they ... References Sources *Reader's Digest "Book of Skills & Too ...
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