# Set square

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.

triangle, set square

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°.

## Geodreieck

Original Geodreieck

Variant of larger TZ-Dreieck with extra markings

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 [de]" (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 [de] (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.

## References

1. ^ Vollrath, Hans-Joachim (1999). "1. Das Geodreieck und seine Vorfahren". 80. Historische Winkelmeßgeräte in Projekten des Mathematikunterrichts (PDF). Der Mathematikunterricht (in German). Vol. 45. pp. 42–58 [3–10]. Archived from the original (PDF) on 2017-11-07. Retrieved 2017-11-07. (29 pages)
2. ^ Vollrath, Hans-Joachim (2006). "Das Geometrie-Dreieck" (in German). Institut für Mathematik, Universität Würzburg. Archived from the original on 2009-04-05. Retrieved 2021-07-11.
3. ^ a b c d Willner, Johannes (2021-03-14). Written at Gießen, Germany. "Mittelständler Aristo: Dieses Unternehmen hat das Geodreieck erfunden". Wirtschaft. Frankfurter Allgemeine Zeitung (FAZ) (in German). Frankfurt am Main, Germany. Archived from the original on 2021-05-19. Retrieved 2021-07-12.
4. ^ "Unternehmen / Geschichte" (in German). GEOtec Zeichen- und Kunststofftechnik GmbH. 2013. Archived from the original on 2021-07-11. Retrieved 2015-08-28. […] 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 […]
5. ^ Bergmayr, Thomas (2019-09-11). "Das Geodreieck kommt aus Tirol". Der Standard (in Austrian German). No. Journal 9291. p. 15.
6. ^ Praxmarer, Christoph (2019-09-09). "Das Geodreieck – das Original aus Wörgl". Wirtschaft. tirol.orf.at (in Austrian German). Österreichischer Rundfunk (ORF). Archived from the original on 2021-07-12. Retrieved 2021-07-12.
7. ^ Hrdina, Jasmine (2021-04-04). "Firma Geotec plant Neustart". top.tirol (in Austrian German). Innsbruck, Austria: Target Group Publishing GmbH. Archived from the original on 2021-07-12. Retrieved 2021-07-12.
8. ^ Walz, Guido (2017) [2016-11-18]. "Geodreieck". Lexikon der Mathematik (in German). Vol. 2: Eig bis Inn (2 ed.). Springer Spektrum / Springer Verlag GmbH. ISBN 978-3-66253503-5. Archived from the original on 2021-07-12. Retrieved 2021-07-12.