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Straightedge
A straightedge or straight edge is a tool used for drawing straight lines, or checking their straightness. If it has equally spaced markings along its length, it is usually called a ruler. Straightedges are used in the automotive service and machining industry to check the flatness of machined mating surfaces. They are also used in the decorating industry for cutting and hanging wallpaper. True straightness can in some cases be checked by using a laser line level as an optical straightedge: it can illuminate an accurately straight line on a flat surface such as the edge of a plank or shelf. A pair of straightedges called winding sticks are used in woodworking to make warping easier to perceive in pieces of wood. Three straight edges can be used to test and calibrate themselves to a certain extent, however this procedure does not control twist. For accurate calibration of a straight edge, a surface plate must be used. Compass-and-straightedge construction An idealized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Poncelet–Steiner Theorem
In the branch of mathematics known as Euclidean geometry, the Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions having additional restrictions imposed on the traditional rules. This result, related to the rusty compass equivalence and to Steiner constructions, states that whatever can be constructed by straightedge and compass (drafting), compass together can be constructed by straightedge alone, provided that a single circle and its centre_(geometry), centre are given: : ''Any Euclidean construction, insofar as the given and required elements are points (or lines), if it can be completed with both the compass and the straightedge together, may be completed with the straightedge alone provided that no fewer than one circle with its center exist in the plane.'' Though a compass can make constructions significantly easier, it is implied that there is no functional purpose of the compass once the first circle has been drawn; the co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Compass-and-straightedge Construction
In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a compass. The idealized ruler, known as a straightedge, is assumed to be infinite in length, have only one edge, and no markings on it. The compass is assumed to have no maximum or minimum radius, and is assumed to "collapse" when lifted from the page, so it may not be directly used to transfer distances. (This is an unimportant restriction since, using a multi-step procedure, a distance can be transferred even with a collapsing compass; see compass equivalence theorem. Note however that whilst a non-collapsing compass held against a straightedge might seem to be equivalent to marking it, the neusis construction is still impermissible and this is what unmarked really means: see Markable rulers below.) More formally, the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Euclidean Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. One of those is the parallel postulate which relates to parallel lines on a Euclidean plane. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logic, logical system in which each result is ''mathematical proof, proved'' from axioms and previously proved theorems. The ''Elements'' begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called algebra and number theory ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Ruler
A ruler, sometimes called a rule, scale, line gauge, or metre/meter stick, is an instrument used to make length measurements, whereby a length is read from a series of markings called "rules" along an edge of the device. Usually, the instrument is rigid and the edge itself is a straightedge ("ruled straightedge"), which additionally allows one to draw straighter lines. Rulers are an important tool in geometry, geography and mathematics. They have been used since at least 2650 BC. Variants Rulers have long been made from different materials and in multiple sizes. Historically, they were mainly wood but plastics have also been used. They can be created with length markings instead of being wikt:scribe, scribed. Metal is also used for more durable rulers for use in the workshop; sometimes a metal edge is embedded into a wooden desk ruler to preserve the edge when used for straight-line cutting. Typically in length, though some can go up to 100 cm, it is useful for a ruler to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Compass (drafting)
A compass, also commonly known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or Arc (geometry), arcs. As caliper#Divider caliper, dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses can be used for mathematics, technical drawing, drafting, navigation and other purposes. Prior to computerization, compasses and other tools for manual drafting were often packaged as a set with interchangeable parts. By the mid-twentieth century, Technical drawing tool#Templates, circle templates supplemented the use of compasses. Today those 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. Construction and parts Compasses are usually made of metal or plastic, and consist of two "legs" connected by a hinge which can be adjusted to allow changing of the radius of the circle drawn. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematical Tools
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a ''proof'' consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstracti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Geometrography
In the mathematical field of geometry, geometrography is the study of geometrical constructions. The concepts and methods of geometrography were first expounded by Émile Lemoine (1840–1912), a French civil engineer and a mathematician, in a meeting of the French Association for the Advancement of the Sciences held at Oran in 1888. Lemoine later expanded his ideas in another memoir read at the Pau meeting of the same Association held in 1892. It is well known in elementary geometry that certain geometrical constructions are simpler than certain others. But in many case it turns out that the apparent simplicity of a construction does not consist in the practical execution of the construction, but in the brevity of the statement of what has to be done. Can then any objective criterion be laid down by which an estimate may be formed of the relative simplicity of several different constructions for attaining the same end? Lemoine developed the ideas of geometrography to answer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Chalk Line
A chalk line or chalk box is a tool for marking long, straight lines on relatively flat surfaces, much further than is practical by hand or with a straightedge. They may be used to lay out straight lines between two points, or vertical lines by using the weight of the line reel as a plumb line. It is an important tool in carpentry, and the working of timber in a rough and unplaned state, as it does not require the timber to have a straight or squared edge formed onto it beforehand. Use A chalk line creates straight lines by the action of a taut Twine, string that has been previously coated with a loose, powdered dye, usually chalk. The string is then laid across the surface to be marked and pulled tight. Next, the string is wikt:pluck, plucked or snapped sharply, causing it to strike the surface, which then transfers its chalk to the surface along the straight line where it struck. Chalk lines are typically used to mark relatively flat surfaces. However, as long as the line is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Surface Plate
A surface plate is a solid, flatness (manufacturing), flat wiktionary:plate, plate used as the main horizontal datum reference, reference plane for precision inspection, marking out (layout), and tooling setup. The surface plate is often used as the baseline for all measurements to a workpiece, therefore one primary surface is finished extremely flat. For example, a grade 0 surface plate may only have a deviation from flatness over a area. Surface plates are a common tool in the manufacturing industry and are often fitted with mounting points so that it can be an integrated structural element of a machine such as a coordinate-measuring machine, precision optical assembly, or other high precision scientific & industrial machine. Plates are typically square or rectangular, although they may be cut to any shape. Accuracy and grade There are varying grades used to describe the accuracy of some metrology equipment such as: AA, A, B, and Workshop grade. While workshop grade is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Winding Stick
In woodworking and carpentry, a pair of winding sticks is a tool that aids in viewing twist (also known as ''wind'') in pieces of lumber by amplifying the defect.Ellis, George. ''Modern Practical Joinery''. London: B.T. Batsford, 1902. 51. Print. 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 to Holtzapffel, Charles. ''Turning and Mechanical Manipulation Intended as a Work of General Reference and Practical Instruction, on the Lathe, and the Various Mechanical Pursuits Followed by Amateurs''. Vol. 2. London: Holtzapffel & Co., 1856. 500. Print. long, tall and tapered in their height from to . The longer the winding sticks, the more they will amplify the wind. It is common for a woodworker to make a matching pair for the purpose, and contrasting colors of woods improve the discernability of differences in level between t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 and cabinetry industries. 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, rather than a pinpoint beam. The axis of the laser is offset from the wall, so that a pinpoint beam would be parallel to and offset from the wall, and would not illuminate it; the fanned beam will intersect the wall, creating an accurately horizontal (or vertical) illuminated line along it. The machine is set up using the built-in spirit level or plumb bob, and the line along the surface is then guaranteed to be accurately horizontal or vertical to within a certain tolerance, specified eithe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
