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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] |
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 pair of 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 really means: see Markable rulers below.) More formally, ... [...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 u ... [...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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Architectural Scale
Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and constructing buildings or other structures. The term comes ; ; . Architectural works, in the material form of buildings, are often perceived as cultural symbols and as works of art. Historical civilizations are often identified with their surviving architectural achievements. The practice, which began in the prehistoric era, has been used as a way of expressing culture for civilizations on all seven continents. For this reason, architecture is considered to be a form of art. Texts on architecture have been written since ancient times. The earliest surviving text on architectural theories is the 1st century AD treatise ''De architectura'' by the Roman architect Vitruvius, according to whom a good building embodies , and (durability, utility, and beauty). Centu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metalworking Measuring Instruments
Metalworking is the process of shaping and reshaping metals to create useful objects, parts, assemblies, and large scale structures. As a term it covers a wide and diverse range of processes, skills, and tools for producing objects on every scale: from huge ships, buildings, and bridges down to precise engine parts and delicate jewelry. The historical roots of metalworking predate recorded history; its use spans cultures, civilizations and millennia. It has evolved from shaping soft, native metals like gold with simple hand tools, through the smelting of ores and hot forging of harder metals like iron, up to highly technical modern processes such as machining and welding. It has been used as an industry, a driver of trade, individual hobbies, and in the creation of art; it can be regarded as both a science and a craft. Modern metalworking processes, though diverse and specialized, can be categorized into one of three broad areas known as forming, cutting, or joining processes. Mo ... [...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 t ... [...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 Civil engineer, 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, Pyrénées-Atlantiques, 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 develope ... [...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 ... [...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 drawing ... [...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 ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''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. 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, explained in geometrical language. For more than two thousand years, the adjective " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
