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 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, an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.
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.
In geometry, a triangular prism or trigonal prism is a prism with 2 triangular bases. If the edges pair with each triangle's vertex and if they are perpendicular to the base, it is a right triangular prism. A right triangular prism may be both semiregular and uniform.
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle, and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle , the sine and cosine functions are denoted as and .
Loewe Technology GmbH, doing business as Loewe, is a German company that develops, designs, manufactures, and sells consumer electronics and electromechanical products and systems. The company was founded in Berlin, in 1923, by brothers Siegmund and David L. Loewe. Since 1948, the company has based its headquarters and production facilities in the Bavarian town of Kronach, Upper Franconia.
Trigonometry is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, 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.
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 encompass many of those offered by combination squares, try squares, and framing squares. 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.
Norbert Pümpel is a visual artist who lives and works in Drosendorf an der Thaya in Austria.
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.
Johann Grander was the Austrian inventor of a water revitalization technology, which has scientifically been proven as ineffective.
The Best Secret GmbH, a subsidiary of Schustermann & Borenstein GmbH, is an e-commerce company for designer merchandise based in Dornach, Germany. Best Secret functions as a closed shopping community.
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.
[…] 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 […]
