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.
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 maximum of 180°.
In some European countries a common form of set square combines a 90-45-45 triangle, a ruler and a protractor into a single tool made of stiff or slightly flexible transparent plastic. [1] [2] [3] Being a mandatory tool used by pupils in middle school and higher in German-speaking and neighbouring countries, this specific design is named " Geodreieck " (short form of "Geometrie-Dreieck", meaning "geometry triangle") or similar. [3] It was originally developed in 1964 by the German-Austrian manufacturer Dennert & Pape Aristo-Werke (after several refirmations now Geotec Schul- und Bürowaren GmbH). [4] [5] [6] [3] [7] Relatively uncommon in English-speaking countries, this is sometimes called a "protractor triangle", a term, however, also used for other similar designs. The original design has a hypotenuse length of 15.8 cm and features a 2×7 cm symmetry scale in millimeter and degree raster. [3] Variants in larger sizes, with fixed or detachable handles, with or without bevelled edges (facets), and with or without ink nodules or embossed labels exist as well. Some variants have extra markings at angles of 7° and 42° (138° and 173°) in addition to the normal 45° and 90° markings to ease dimetric axonometry per ISO 5456-3, [8] others feature angle scales in gons instead of degrees. Several other somewhat similar designs named "TZ-Dreieck" ("TZ triangle") exist for (larger) technical drawings (TZ from German: Technisches Zeichnen). The scale reaches from 10 to 10 cm, or even 11 to 11 cm.
Similar to the Geodreieck, a number of other protractor triangle types exist for navigation purposes. Various designs are named navigation (protractor) triangle, nautical navigational triangle, nautical set square, Portland (navigational) triangle or Portland protractor triangle, Kent-type triangle, Inoue-type A/B nautical triangle or plotting triangle, course triangle, yachtsmen triangle, and supporting triangle.
However, some widely used navigational protractors, such as the Cras protractor, are not triangles.
A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular, forming a right angle.
In geometry and trigonometry, a right angle is an angle of exactly 90 degrees or /2 radians corresponding to a quarter turn. If a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. The term is a calque of Latin angulus rectus; here rectus means "upright", referring to the vertical perpendicular to a horizontal base line.
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 protractor is a commonly used type in the fields of mechanics, engineering, and geometry.
In mathematics, the Lévy C curve is a self-similar fractal curve that was first described and whose differentiability properties were analysed by Ernesto Cesàro in 1906 and Georg Faber in 1910, but now bears the name of French mathematician Paul Lévy, who was the first to describe its self-similarity properties as well as to provide a geometrical construction showing it as a representative curve in the same class as the Koch curve. It is a special case of a period-doubling curve, a de Rham curve.
The steel square is a tool used in carpentry. Carpenters use various tools to lay out structures that are square, many of which are made of steel, but the name steel square refers to a specific long-armed square that has additional uses for measurement, especially of various angles. It consists of a long, wider arm and a shorter, narrower arm, which meet at an angle of 90 degrees. Today the steel square is more commonly referred to as the framing square or carpenter's square, and such squares are no longer invariably made of steel ; they can also be made of aluminum or polymers, which are light and resistant to rust.
In geometry, the Malfatti circles are three circles inside a given triangle such that each circle is tangent to the other two and to two sides of the triangle. They are named after Gian Francesco Malfatti, who made early studies of the problem of constructing these circles in the mistaken belief that they would have the largest possible total area of any three disjoint circles within the triangle.
Trigonometry is a branch of mathematics concerned with relationships between angles and side lengths of triangles. More specifically, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios such as sine.
Deutsche Wirtschaftsbetriebe, abbreviated DWB, was a project launched by Nazi Germany in World War II. Organised and managed by the Allgemeine SS, its aim was to profit from the use of slave labour extracted from the Nazi concentration camp inmates.
SM UB-19 was a German Type UB II submarine or U-boat in the German Imperial Navy during World War I. The U-boat was ordered on 30 April 1915 and launched on 2 September 1915. She was commissioned into the German Imperial Navy on 16 December 1915 as SM UB-19. The submarine sank 13 ships in 15 patrols for a total of 10,040 gross register tons (GRT). UB-19 was sunk in the English Channel at 49°56′N2°45′W on 30 November 1916 by British Q ship HMS Penshurst.
SM UB-20 was a German Type UB II submarine or U-boat in the German Imperial Navy during World War I. The U-boat was ordered on 30 April 1915 and launched on 26 September 1915. She was commissioned into the German Imperial Navy on 10 February 1916 as SM UB-20. The submarine sank 13 ships in 15 patrols for a total of 10,230 gross register tons (GRT). UB-20 was mined and sunk on 28 July 1917 at 51°21′N2°38′E. Fifteen crew members died in the event.
SM UB-41 was a German Type UB II submarine or U-boat in the German Imperial Navy during World War I.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
A speed square, also called a rafter square, rafter angle square, and triangle square, is a multi-purpose triangular carpenters' tool used for marking out. Its functions include many of those of a combination square, try square, and framing square. Carpenters use it to make basic measurements and mark lines on dimensional lumber, and as a saw guide for short 45 and 90 degree cuts.
The rule of marteloio is a medieval technique of navigational computation that uses compass direction, distance and a simple trigonometric table known as the toleta de marteloio. The rule told mariners how to plot the traverse between two different navigation courses by means of resolving triangles with the help of the Toleta and basic arithmetic.
In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape. The term was coined as a pun on animal reptiles by recreational mathematician Solomon W. Golomb and popularized by Martin Gardner in his "Mathematical Games" column in the May 1963 issue of Scientific American. In 2012 a generalization of rep-tiles called self-tiling tile sets was introduced by Lee Sallows in Mathematics Magazine.
SM UB-129 was a German Type UB III submarine or U-boat in the German Imperial Navy during World War I. She was commissioned into the German Imperial Navy on 11 June 1918 as SM UB-129.
EKO Stahl is a steelworks in Eisenhüttenstadt, Brandenburg, Germany. It was established by the East German government in the early 1950s on a greenfield site, initially producing only pig iron. The name was changed in 1961 from Eisenhuttenkombinat 'J.W. Stalin' to Eisenhüttenkombinat Ost (EKO).
Vertical declining dials are sundials that indicate local apparent time. Vertical south dials are a special case: as are vertical north, vertical east and vertical west dials. The word declining means that the wall is offset from one of these 4 cardinal points. There are dials that are not vertical, and these are called reclining dials.
The Lotschnittaxiom is an axiom in the foundations of geometry, introduced and studied by Friedrich Bachmann. It states:
Perpendiculars raised on each side of a right angle intersect.
Marquois scales are a mathematical instrument that found widespread use in Britain, particularly in military surveying, from the late 18th century to World War II.
{{cite book}}: |journal= ignored (help) (29 pages)[…] 1964 […] Das klassische Geodreieck wird entwickelt und als international registrierte und geschützte Marke eingetragen. Inzwischen millionenfach gefertigt und in vielen Ländern zum Standard-Zeichengerät in der Schule und Ausbildung avanciert […]
