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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. 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 straightedge is used in compass-and-straightedge constructions in plane geometry. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 states that whatever can be constructed by straightedge and compass together can be constructed by straightedge alone, provided that a single circle and its centre are given. This theorem is related to the rusty compass equivalence. : ''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. All constructions remain possible, though it is naturally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 Idealization (science philosophy), idealized ruler and a pair of Compass (drawing tool), compasses. 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 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the ''Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions ( theorems) from these. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logical system in which each result is '' 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, explained in geometrical language. For more than two thousand years, the adjective "Euclidean" was unnecessary because no other sort of geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruler
A ruler, sometimes called a rule, line gauge, or scale, is a device used in geometry and technical drawing, as well as the engineering and construction industries, to measure distances or draw straight lines. Variants Rulers have long been made from different materials and in multiple sizes. Some are wooden. Plastics have also been 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; sometimes a metal edge is embedded into a wooden desk ruler to preserve the edge when used for straight-line cutting. 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., , 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compass (drafting)
A compass, more accurately known as a pair of compasses, is a technical drawing instrument that can be used for inscribing circles or arcs. As dividers, it can also be used as a tool to mark out distances, in particular, on maps. Compasses can be used for mathematics, 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, 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. Typically one leg has a spike at its end for anchoring, and the other leg holds a draw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stonemasonry Tools
Stonemasonry or stonecraft is the creation of buildings, structures, and sculpture using stone as the primary material. It is one of the oldest activities and professions in human history. Many of the long-lasting, ancient shelters, temples, monuments, artifacts, fortifications, roads, bridges, and entire cities were built of stone. Famous works of stonemasonry include the Egyptian pyramids, the Taj Mahal, Cusco's Incan Wall, Easter Island's statues, Angkor Wat, Borobudur, Tihuanaco, Tenochtitlan, Persepolis, the Parthenon, Stonehenge, the Great Wall of China, and Chartres Cathedral. Definition Masonry is the craft of shaping rough pieces of rock into accurate geometrical shapes, at times simple, but some of considerable complexity, and then arranging the resulting stones, often together with mortar, to form structures. *Quarrymen split sheets of rock, and extract the resulting blocks of stone from the ground. *Sawyers cut these rough blocks into cuboids, to required siz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chalk Line
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. 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, 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 draws straight lines by the action of a taut nylon or similar string that has been previously coated with a loose dye, usually chalk. 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 typically used to mark relatively flat surfaces. However, as long as the line is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Surface Plate
A surface plate is a solid, flat plate used as the main horizontal 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 with tolerances below per 2960 mm for a grade 0 plate. 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 the least accurate, all grades of surface plates are held to a high degree of flatness. Surface pla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 eith ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
