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- Angle_trisection abstract "Angle trisection is a classic problem of compass and straightedge constructions of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge, and a compass. The problem as stated is generally impossible to solve, as shown by Pierre Wantzel (1837). Wantzel's proof relies on ideas from the field of Galois theory—in particular, trisection of an angle corresponds to the solution of a certain cubic equation, which is not possible using the given tools. Note that the fact that there is no way to trisect an angle in general with just a compass and a straightedge does not mean that there is no trisectible angle: for example, it is relatively straightforward to trisect a right angle (that is, to construct an angle of measure 30 degrees).It is, however, possible to trisect an arbitrary angle, but using tools other than straightedge and compass. For example, neusis construction, also known to ancient Greeks, involves simultaneous sliding and rotation of a marked straightedge, which cannot be achieved with the original tools. Other techniques were developed by mathematicians over centuries.Because it is defined in simple terms, but complex to prove unsolvable, the problem of angle trisection is a frequent subject of pseudomathematical attempts at solution by naive enthusiasts. The "solutions" often involve mistaken interpretations of the rules, or are simply incorrect.".
- Angle_trisection thumbnail Neusis-trisection.svg?width=300.
- Angle_trisection wikiPageExternalLink AngleTrisection.html.
- Angle_trisection wikiPageExternalLink GeometricProblemsofAntiquity.html.
- Angle_trisection wikiPageExternalLink trisectlimacon.webs.com.
- Angle_trisection wikiPageExternalLink Trisecting_an_angle.html.
- Angle_trisection wikiPageExternalLink archi.shtml.
- Angle_trisection wikiPageExternalLink angtri.
- Angle_trisection wikiPageExternalLink trisect.htm.
- Angle_trisection wikiPageExternalLink mathtrek.asp.
- Angle_trisection wikiPageExternalLink Star-of-David-Flower-of-Life.html.
- Angle_trisection wikiPageExternalLink trisect.HTM.
- Angle_trisection wikiPageExternalLink 5knI8nq2l.
- Angle_trisection wikiPageExternalLink conchoidOfNicomedes.html.
- Angle_trisection wikiPageID "91111".
- Angle_trisection wikiPageRevisionID "602948061".
- Angle_trisection hasPhotoCollection Angle_trisection.
- Angle_trisection subject Category:Articles_containing_proofs.
- Angle_trisection subject Category:Compass_and_straightedge_constructions.
- Angle_trisection subject Category:Euclidean_plane_geometry.
- Angle_trisection subject Category:History_of_geometry.
- Angle_trisection subject Category:Mathematical_problems.
- Angle_trisection type Abstraction100002137.
- Angle_trisection type Attribute100024264.
- Angle_trisection type Condition113920835.
- Angle_trisection type Difficulty114408086.
- Angle_trisection type MathematicalProblems.
- Angle_trisection type Problem114410605.
- Angle_trisection type State100024720.
- Angle_trisection comment "Angle trisection is a classic problem of compass and straightedge constructions of ancient Greek mathematics. It concerns construction of an angle equal to one third of a given arbitrary angle, using only two tools: an unmarked straightedge, and a compass. The problem as stated is generally impossible to solve, as shown by Pierre Wantzel (1837).".
- Angle_trisection label "Angle trisection".
- Angle_trisection label "Dreiteilung des Winkels".
- Angle_trisection label "Driedeling van de hoek".
- Angle_trisection label "Trisección del ángulo".
- Angle_trisection label "Trisection de l'angle".
- Angle_trisection label "Trisezione dell'angolo".
- Angle_trisection label "Trissecção do ângulo".
- Angle_trisection label "Trysekcja kąta".
- Angle_trisection label "Трисекция угла".
- Angle_trisection label "تثليث الزاوية".
- Angle_trisection label "三等分角".
- Angle_trisection sameAs Trisekce_úhlu.
- Angle_trisection sameAs Dreiteilung_des_Winkels.
- Angle_trisection sameAs Trisección_del_ángulo.
- Angle_trisection sameAs Trisection_de_l'angle.
- Angle_trisection sameAs Trisezione_dell'angolo.
- Angle_trisection sameAs 각의_3등분.
- Angle_trisection sameAs Driedeling_van_de_hoek.
- Angle_trisection sameAs Trysekcja_kąta.
- Angle_trisection sameAs Trissecção_do_ângulo.
- Angle_trisection sameAs m.02wv6cd.
- Angle_trisection sameAs Q733081.
- Angle_trisection sameAs Q733081.
- Angle_trisection sameAs Angle_trisection.
- Angle_trisection wasDerivedFrom Angle_trisection?oldid=602948061.
- Angle_trisection depiction Neusis-trisection.svg.
- Angle_trisection isPrimaryTopicOf Angle_trisection.