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<title>Set square</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Set square</span></span>

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</style><div role="note" class="hatnote navigation-not-searchable">For the British business incubator network, see <a href="SETsquared" title="SETsquared">SETsquared</a>.</div>

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<p>A <b>set square</b> or <b>triangle</b> (<a href="American_English" title="American English">American English</a>) is an object used in engineering and <a href="Technical_drawing" title="Technical drawing">technical drawing</a>, with the aim of providing a <a href="Straightedge" title="Straightedge">straightedge</a> at a <a href="Right_angle" title="Right angle">right angle</a> or other particular planar angle to a <a href="https://en.wiktionary.org/wiki/baseline" class="extiw external" title="wikt:baseline">baseline</a>.

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<div class="mw-heading mw-heading2"><h2 id="Types">Types</h2></div>

<p>The simplest form of set square is a triangular piece of transparent <a href="Plastic" title="Plastic">plastic</a> (or formerly of polished wood) with the centre removed. More commonly the set square bears the markings of a <a href="Ruler" title="Ruler">ruler</a> and a half circle <a href="Protractor" class="mw-redirect" title="Protractor">protractor</a>. The outer edges are typically <a href="Bevel" title="Bevel">bevelled</a>. These set squares come in two usual forms, both <a href="Right_triangle" title="Right triangle">right triangles</a>: one with 90-45-45 degree angles, the other with 30-60-90 degree angles. Combining the two forms by placing the <a href="Hypotenuse" title="Hypotenuse">hypotenuses</a> together will also yield 15° and 75° angles. They are often purchased in packs with <a href="Protractor" class="mw-redirect" title="Protractor">protractors</a> and <a href="Compass_(drafting)" class="mw-redirect" title="Compass (drafting)">compasses</a>.

</p><p>Less commonly found is the adjustable set square. Here, the body of the object is cut in half and rejoined with a <a href="Hinge" title="Hinge">hinge</a> marked with angles. Adjustment to the marked angle will produce any desired angle up to a maximum of 180°.

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<div class="mw-heading mw-heading2"><h2 id="Geodreieck"><span title="German-language text"><i lang="de">Geodreieck</i></span></h2></div>

<p>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.<sup id="cite_ref-Vollrath_1999_1-0" class="reference"><a href="#cite_note-Vollrath_1999-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Vollrath_2006_2-0" class="reference"><a href="#cite_note-Vollrath_2006-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Willner_2021_3-0" class="reference"><a href="#cite_note-Willner_2021-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Being a mandatory tool used by pupils in <a href="Middle_school" title="Middle school">middle school</a> and higher in German-speaking and neighbouring countries, this specific design is named "<span title="German-language text"><i lang="de"><a href="Geodreieck" class="mw-redirect" title="Geodreieck">Geodreieck</a></i></span>" (short form of "<span title="German-language text"><i lang="de">Geometrie-Dreieck</i></span>", meaning "geometry triangle") or similar.<sup id="cite_ref-Willner_2021_3-1" class="reference"><a href="#cite_note-Willner_2021-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> It was originally developed in 1964 by the German manufacturer Dennert & Pape Aristo-Werke (after several refirmations now <i>Geotec Schul- und Bürowaren GmbH</i>).<sup id="cite_ref-Aristo_2013_4-0" class="reference"><a href="#cite_note-Aristo_2013-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Bergmayr_2019_5-0" class="reference"><a href="#cite_note-Bergmayr_2019-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Praxmarer_2019_6-0" class="reference"><a href="#cite_note-Praxmarer_2019-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Willner_2021_3-2" class="reference"><a href="#cite_note-Willner_2021-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Hrdina_2021_7-0" class="reference"><a href="#cite_note-Hrdina_2021-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> 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 <a href="Millimeter" class="mw-redirect" title="Millimeter">millimeter</a> and <a href="Degree_(angle)" title="Degree (angle)">degree</a> raster.<sup id="cite_ref-Willner_2021_3-3" class="reference"><a href="#cite_note-Willner_2021-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> 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 <a href="Dimetric_projection" class="mw-redirect" title="Dimetric projection">dimetric</a> <a href="Axonometry" title="Axonometry">axonometry</a> per ISO 5456-3,<sup id="cite_ref-Walz_2017_8-0" class="reference"><a href="#cite_note-Walz_2017-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> others feature angle scales in <a href="Gon_(unit)" class="mw-redirect" title="Gon (unit)">gons</a> instead of degrees. Several other somewhat similar designs named "<span title="German-language text"><i lang="de">TZ-Dreieck</i></span>" ("TZ triangle") exist for (larger) technical drawings (TZ from German: <span title="German-language text"><i lang="de">Technisches Zeichnen</i></span>). The scale reaches from 10 to 10 cm, or even 11 to 11 cm.

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<div class="mw-heading mw-heading2"><h2 id="Navigation_protractor_triangles">Navigation protractor triangles</h2></div>

<p>Similar to the <span title="German-language text"><i lang="de">Geodreieck</i></span>, a number of other protractor triangle types exist for <a href="Navigation" title="Navigation">navigation</a> 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.

</p><p>However, some widely used navigational protractors, such as the <a href="Cras_protractor" class="mw-redirect" title="Cras protractor">Cras protractor</a>, are not triangles.

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<ul><li><a href="Speed_square" title="Speed square">Speed square</a></li>

<li><a href="Technical_drawing_tool" title="Technical drawing tool">Technical drawing tool</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFVollrath1999" class="citation book cs1 cs1-prop-interwiki-linked-name cs1-prop-foreign-lang-source"><a href="https://de.wikipedia.org/wiki/Hans-Joachim_Vollrath" class="extiw external" title="de:Hans-Joachim Vollrath">Vollrath, Hans-Joachim</a> <span class="cs1-format">[in German]</span> (1999). "1. Das Geodreieck und seine Vorfahren". <a rel="nofollow" class="external text" href="https://web.archive.org/web/20171107164846/http://www.history.didaktik.mathematik.uni-wuerzburg.de/vollrath/papers/080.pdf"><i>80. Historische Winkelmeßgeräte in Projekten des Mathematikunterrichts</i></a> <span class="cs1-format">(PDF)</span>. Der Mathematikunterricht (in German). Vol. 45. pp. 42–58 [3–10]. Archived from <a rel="nofollow" class="external text" href="http://www.history.didaktik.mathematik.uni-wuerzburg.de/vollrath/papers/080.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2017-11-07<span class="reference-accessdate">. Retrieved <span class="nowrap">2017-11-07</span></span>.</cite> (29 pages)</span>

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<li id="cite_note-Vollrath_2006-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Vollrath_2006_2-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFVollrath2006" class="citation web cs1 cs1-prop-interwiki-linked-name cs1-prop-foreign-lang-source"><a href="https://de.wikipedia.org/wiki/Hans-Joachim_Vollrath" class="extiw external" title="de:Hans-Joachim Vollrath">Vollrath, Hans-Joachim</a> <span class="cs1-format">[in German]</span> (2006). <a rel="nofollow" class="external text" href="https://www.didaktik.mathematik.uni-wuerzburg.de/history/ausstell/winkelmesser/geodreieck.html">"Das Geometrie-Dreieck"</a> (in German). Institut für Mathematik, <a href="Universit%C3%A4t_W%C3%BCrzburg" class="mw-redirect" title="Universität Würzburg">Universität Würzburg</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090405190310/http://www.didaktik.mathematik.uni-wuerzburg.de/history/ausstell/winkelmesser/geodreieck.html">Archived</a> from the original on 2009-04-05<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-07-11</span></span>.</cite></span>

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<li id="cite_note-Willner_2021-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Willner_2021_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Willner_2021_3-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Willner_2021_3-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Willner_2021_3-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><cite id="CITEREFWillner2021" class="citation news cs1 cs1-prop-location-test cs1-prop-foreign-lang-source">Willner, Johannes (2021-03-14). Written at Gießen, Germany. <a rel="nofollow" class="external text" href="https://www.faz.net/aktuell/wirtschaft/unternehmen/geodreieck-das-mittelstaendische-unternehmen-aristo-hat-es-erfunden-17225868.html">"Mittelständler Aristo: Dieses Unternehmen hat das Geodreieck erfunden"</a>. Wirtschaft. <i><a href="Frankfurter_Allgemeine_Zeitung" title="Frankfurter Allgemeine Zeitung">Frankfurter Allgemeine Zeitung</a> (FAZ)</i> (in German). Frankfurt am Main, Germany. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210519191540/https://www.faz.net/aktuell/wirtschaft/unternehmen/geodreieck-das-mittelstaendische-unternehmen-aristo-hat-es-erfunden-17225868.html">Archived</a> from the original on 2021-05-19<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-07-12</span></span>.</cite></span>

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<li id="cite_note-Aristo_2013-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Aristo_2013_4-0">^</a></b></span> <span class="reference-text"><cite class="citation web cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="http://www.aristo.at/go/unternehmen">"Unternehmen / Geschichte"</a> (in German). GEOtec Zeichen- und Kunststofftechnik GmbH. 2013. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210711121831/https://www.aristo.at/unternehmen/">Archived</a> from the original on 2021-07-11<span class="reference-accessdate">. Retrieved <span class="nowrap">2015-08-28</span></span>. <q>[…] 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 […]</q></cite></span>

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<li id="cite_note-Bergmayr_2019-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Bergmayr_2019_5-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFBergmayr2019" class="citation news cs1 cs1-prop-foreign-lang-source">Bergmayr, Thomas (2019-09-11). "Das Geodreieck kommt aus Tirol". <i><a href="Der_Standard" title="Der Standard">Der Standard</a></i> (in Austrian German). No. Journal 9291. p. 15.</cite></span>

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<li id="cite_note-Praxmarer_2019-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Praxmarer_2019_6-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFPraxmarer2019" class="citation web cs1 cs1-prop-foreign-lang-source">Praxmarer, Christoph (2019-09-09). <a rel="nofollow" class="external text" href="https://tirol.orf.at/stories/3010465/">"Das Geodreieck – das Original aus Wörgl"</a>. Wirtschaft. <i>tirol.orf.at</i> (in Austrian German). <a href="%C3%96sterreichischer_Rundfunk" class="mw-redirect" title="Österreichischer Rundfunk">Österreichischer Rundfunk</a> (ORF). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210712111603/https://tirol.orf.at/stories/3010465/">Archived</a> from the original on 2021-07-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-07-12</span></span>.</cite></span>

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<li id="cite_note-Hrdina_2021-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hrdina_2021_7-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFHrdina2021" class="citation web cs1 cs1-prop-foreign-lang-source">Hrdina, Jasmine (2021-04-04). <a rel="nofollow" class="external text" href="https://www.top.tirol/wirtschaftsmeldungen/wirtschaftsnews/firma-geotec-plant-neustart">"Firma Geotec plant Neustart"</a>. <i>top.tirol</i> (in Austrian German). Innsbruck, Austria: Target Group Publishing GmbH. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210712112529/https://www.top.tirol/wirtschaftsmeldungen/wirtschaftsnews/firma-geotec-plant-neustart">Archived</a> from the original on 2021-07-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-07-12</span></span>.</cite></span>

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<li id="cite_note-Walz_2017-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-Walz_2017_8-0">^</a></b></span> <span class="reference-text"><cite id="CITEREFWalz2017" class="citation book cs1 cs1-prop-long-vol cs1-prop-foreign-lang-source">Walz, Guido (2017) [2016-11-18]. "Geodreieck". <a rel="nofollow" class="external text" href="https://www.spektrum.de/lexikon/mathematik/geodreieck/3442"><i>Lexikon der Mathematik</i></a> (in German). Vol. 2: Eig bis Inn (2 ed.). <a href="Springer_Spektrum" class="mw-redirect" title="Springer Spektrum">Springer Spektrum</a> / <a href="Springer_Verlag_GmbH" class="mw-redirect" title="Springer Verlag GmbH">Springer Verlag GmbH</a>. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>978-3-66253503-5</bdi>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210712111202/https://www.spektrum.de/lexikon/mathematik/geodreieck/3442">Archived</a> from the original on 2021-07-12<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-07-12</span></span>.</cite></span>

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<div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Set_squares" class="extiw external" title="commons:Category:Set squares">Set squares</a></span>.</div></div>

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</style><div id="Measuring_and_alignment_tools738" style="font-size:114%;margin:0 4em"><a href="Measuring_instrument" class="mw-redirect" title="Measuring instrument">Measuring</a> and alignment tools</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em">

<ul><li><a href="Architect's_scale" class="mw-redirect" title="Architect's scale">Architect's scale</a></li>

<li><a href="Beam_compass" title="Beam compass">Beam compass</a></li>

<li><a href="Calipers" title="Calipers">Calipers</a></li>

<li><a href="Chalk_line" title="Chalk line">Chalk line</a></li>

<li><a href="Combination_square" title="Combination square">Combination square</a></li>

<li><a href="Compass_(drawing_tool)" title="Compass (drawing tool)">Compass</a></li>

<li><a href="Coordinate-measuring_machine" title="Coordinate-measuring machine">Coordinate-measuring machine</a></li>

<li><a href="Diagonal_scale" class="mw-redirect" title="Diagonal scale">Diagonal scale</a></li>

<li><a href="Drafting_machine" title="Drafting machine">Drafting machine</a></li>

<li><a href="Engineer's_scale" class="mw-redirect" title="Engineer's scale">Engineer's scale</a></li>

<li><a href="Feeler_gauge" title="Feeler gauge">Feeler gauge</a></li>

<li><a href="Flat_spline" title="Flat spline">Flat spline</a></li>

<li><a href="French_curve" title="French curve">French curve</a></li>

<li><a href="Gunter's_chain" title="Gunter's chain">Gunter's chain</a></li>

<li><a href="Laser_level" title="Laser level">Laser level</a></li>

<li><a href="Line_laser_level" title="Line laser level">Line laser level</a></li>

<li><a href="Laser_rangefinder#Laser_measuring_tools" title="Laser rangefinder">Laser measuring tool</a></li>

<li><a href="Lesbian_rule" title="Lesbian rule">Lesbian rule</a></li>

<li><a href="Marking_gauge" title="Marking gauge">Marking gauge</a></li>

<li><a href="Measuring_rod" title="Measuring rod">Measuring rod</a></li>

<li><a href="Meterstick" class="mw-redirect" title="Meterstick">Meterstick</a></li>

<li><a href="Micrometer_(device)" title="Micrometer (device)">Micrometer</a></li>

<li><a href="Plumb_bob" title="Plumb bob">Plumb-bob</a></li>

<li><a href="Goniometer#Protractor" title="Goniometer">Protractor</a></li>

<li><a href="Radius_gauge" title="Radius gauge">Radius gauge</a></li>

<li><a href="Ruler" title="Ruler">Ruler</a></li>

<li><a href="Skirret_(tool)" title="Skirret (tool)">Skirret</a></li>

<li><a href="Sliding_T_bevel" title="Sliding T bevel">Sliding T bevel</a></li>

<li><a href="Speed_square" title="Speed square">Speed square</a></li>

<li><a href="Spirit_level" title="Spirit level">Spirit level</a></li>

<li><a href="Steel_square" title="Steel square">Steel square</a></li>

<li><a href="Stencil" title="Stencil">Stencil</a></li>

<li><a href="Straightedge" title="Straightedge">Straightedge</a></li>

<li><a href="Square_(tool)" title="Square (tool)">Square</a></li>

<li><a href="T-square" title="T-square">T-square</a></li>

<li><a href="Tape_measure" title="Tape measure">Tape measure</a></li>

<li><a href="Theodolite" title="Theodolite">Theodolite</a></li>

<li><a href="Thread_pitch_gauge" title="Thread pitch gauge">Thread pitch gauge</a></li>

<li><a href="Try_square" title="Try square">Try square</a></li>

<li><a href="Vernier_scale" title="Vernier scale">Vernier scale</a></li>

<li><a href="Weighing_scale" title="Weighing scale">Weighing scale</a></li>

<li><a href="Wiggler_(tool)" title="Wiggler (tool)">Wiggler</a></li>

<li><a href="Winding_stick" title="Winding stick">Winding sticks</a></li></ul>

</div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><div class="hlist">

<dl><dt>Types of tools</dt>

<dd>Cleaning</dd>

<dd>Cutting and abrasive</dd>

<dd>Forestry</dd>

<dd>Garden</dd>

<dd>Kitchen</dd>

<dd>Machine and metalworking</dd>

<dd>Masonry</dd>

<dd>Measuring and alignment</dd>

<dd>Mining</dd>

<dd>Power</dd>

<dd>Textile</dd>

<dd>Woodworking</dd></dl>

</div></div></td></tr></tbody></table></div></div><div><div class="zim-footer">

This article is issued from <a class="external text" title="Last edited on 2024-11-20" href="https://en.wikipedia.org/wiki/?title=Set_square&oldid=1258627760">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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