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- Compass-and-straightedge_construction abstract "Compass-and-straightedge or ruler-and-compass construction is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.The idealized ruler, known as a straightedge, is assumed to be infinite in length, and has no markings on it and only one edge. The compass is assumed to collapse when lifted from the page, so may not be directly used to transfer distances. (This is an unimportant restriction, as this may be achieved via the compass equivalence theorem.) More formally, the only permissible constructions are those granted by Euclid's first three postulates.Every point constructible using straightedge and compass may be constructed using compass alone. A number of ancient problems in plane geometry impose this restriction.The most famous straightedge-and-compass problems have been proven impossible in several cases by Pierre Wantzel in 1837, using the mathematical theory of fields. In spite of existing proofs of impossibility, some persist in trying to solve these problems. Many of these problems are easily solvable provided that other geometric transformations are allowed: for example, doubling the cube is possible using geometric constructions, but not possible using straightedge and compass alone.".
- Compass-and-straightedge_construction thumbnail Regular_Hexagon_Inscribed_in_a_Circle_240px.gif?width=300.
- Compass-and-straightedge_construction wikiPageExternalLink books?id=ngAAAAAAMBAJ&pg=PA104.
- Compass-and-straightedge_construction wikiPageExternalLink faq.regpoly.html.
- Compass-and-straightedge_construction wikiPageExternalLink wims.cgi?&+lang=en&+module=tool%2Fgeometry%2Frulecomp.fr.
- Compass-and-straightedge_construction wikiPageExternalLink Doubling_the_cube.html.
- Compass-and-straightedge_construction wikiPageExternalLink Squaring_the_circle.html.
- Compass-and-straightedge_construction wikiPageExternalLink Hippocrates.shtml.
- Compass-and-straightedge_construction wikiPageExternalLink compass.shtml.
- Compass-and-straightedge_construction wikiPageExternalLink archi.shtml.
- Compass-and-straightedge_construction wikiPageExternalLink trisect.htm.
- Compass-and-straightedge_construction wikiPageExternalLink constructionstoc.html.
- Compass-and-straightedge_construction wikiPageExternalLink straightedge-and-compass.
- Compass-and-straightedge_construction wikiPageID "61229".
- Compass-and-straightedge_construction wikiPageRevisionID "600178972".
- Compass-and-straightedge_construction title "Angle Trisection".
- Compass-and-straightedge_construction urlname "AngleTrisection".
- Compass-and-straightedge_construction subject Category:Compass_and_straightedge_constructions.
- Compass-and-straightedge_construction subject Category:Euclidean_plane_geometry.
- Compass-and-straightedge_construction comment "Compass-and-straightedge or ruler-and-compass construction is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.The idealized ruler, known as a straightedge, is assumed to be infinite in length, and has no markings on it and only one edge. The compass is assumed to collapse when lifted from the page, so may not be directly used to transfer distances.".
- Compass-and-straightedge_construction label "Compass-and-straightedge construction".
- Compass-and-straightedge_construction label "Constructie met passer en liniaal".
- Compass-and-straightedge_construction label "Construction à la règle et au compas".
- Compass-and-straightedge_construction label "Construções com régua e compasso".
- Compass-and-straightedge_construction label "Costruzioni con riga e compasso".
- Compass-and-straightedge_construction label "Konstrukcje klasyczne".
- Compass-and-straightedge_construction label "Konstruktion mit Zirkel und Lineal".
- Compass-and-straightedge_construction label "Regla y compás".
- Compass-and-straightedge_construction label "Построение с помощью циркуля и линейки".
- Compass-and-straightedge_construction label "إنشاءات الفرجار والمسطرة".
- Compass-and-straightedge_construction label "定規とコンパスによる作図".
- Compass-and-straightedge_construction label "尺规作图".
- Compass-and-straightedge_construction sameAs Eukleidovská_konstrukce.
- Compass-and-straightedge_construction sameAs Konstruktion_mit_Zirkel_und_Lineal.
- Compass-and-straightedge_construction sameAs Regla_y_compás.
- Compass-and-straightedge_construction sameAs Construction_à_la_règle_et_au_compas.
- Compass-and-straightedge_construction sameAs Costruzioni_con_riga_e_compasso.
- Compass-and-straightedge_construction sameAs 定規とコンパスによる作図.
- Compass-and-straightedge_construction sameAs 작도.
- Compass-and-straightedge_construction sameAs Constructie_met_passer_en_liniaal.
- Compass-and-straightedge_construction sameAs Konstrukcje_klasyczne.
- Compass-and-straightedge_construction sameAs Construções_com_régua_e_compasso.
- Compass-and-straightedge_construction sameAs m.0gm1t.
- Compass-and-straightedge_construction sameAs Q115368.
- Compass-and-straightedge_construction sameAs Q115368.
- Compass-and-straightedge_construction wasDerivedFrom Compass-and-straightedge_construction?oldid=600178972.
- Compass-and-straightedge_construction depiction Regular_Hexagon_Inscribed_in_a_Circle_240px.gif.
- Compass-and-straightedge_construction isPrimaryTopicOf Compass-and-straightedge_construction.
