Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Angle_trisection> ?p ?o }
- 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 in 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 by 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.
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- 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 wikiPageExternalLink trisecting-angle-origami.
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- Angle_trisection wikiPageRevisionID "683042000".
- Angle_trisection wikiPageWikiLink Angle.
- Angle_trisection wikiPageWikiLink Archimedean_Spiral.
- Angle_trisection wikiPageWikiLink Archimedean_spiral.
- Angle_trisection wikiPageWikiLink Archimedes.
- Angle_trisection wikiPageWikiLink Bisection.
- Angle_trisection wikiPageWikiLink Blaise_Pascal.
- Angle_trisection wikiPageWikiLink Category:Articles_containing_proofs.
- Angle_trisection wikiPageWikiLink Category:Compass_and_straightedge_constructions.
- Angle_trisection wikiPageWikiLink Category:Euclidean_plane_geometry.
- Angle_trisection wikiPageWikiLink Category:History_of_geometry.
- Angle_trisection wikiPageWikiLink Category:Mathematical_problems.
- Angle_trisection wikiPageWikiLink Compass-and-straightedge_construction.
- Angle_trisection wikiPageWikiLink Compass_(drafting).
- Angle_trisection wikiPageWikiLink Compass_(drawing_tool).
- Angle_trisection wikiPageWikiLink Compass_and_straightedge_constructions.
- Angle_trisection wikiPageWikiLink Conchoid_(mathematics).
- Angle_trisection wikiPageWikiLink Constructible_number.
- Angle_trisection wikiPageWikiLink Constructible_polygon.
- Angle_trisection wikiPageWikiLink Cubic_equation.
- Angle_trisection wikiPageWikiLink Cubic_function.
- Angle_trisection wikiPageWikiLink Cubic_polynomial.
- Angle_trisection wikiPageWikiLink Degree_(angle).
- Angle_trisection wikiPageWikiLink Doubling_the_cube.
- Angle_trisection wikiPageWikiLink Equilateral_triangle.
- Angle_trisection wikiPageWikiLink Euclidean_geometry.
- Angle_trisection wikiPageWikiLink Fermat_number.
- Angle_trisection wikiPageWikiLink Fermat_prime.
- Angle_trisection wikiPageWikiLink Field_(mathematics).
- Angle_trisection wikiPageWikiLink Field_extension.
- Angle_trisection wikiPageWikiLink File:Bisection_construction.gif.
- Angle_trisection wikiPageWikiLink Galois_theory.
- Angle_trisection wikiPageWikiLink Geometric_cryptography.
- Angle_trisection wikiPageWikiLink Greek_mathematics.
- Angle_trisection wikiPageWikiLink History_of_geometry.
- Angle_trisection wikiPageWikiLink Huzitas_axioms.
- Angle_trisection wikiPageWikiLink Huzita–Hatori_axioms.
- Angle_trisection wikiPageWikiLink Hypothesis.
- Angle_trisection wikiPageWikiLink If_and_only_if.
- Angle_trisection wikiPageWikiLink Intercept_theorem.
- Angle_trisection wikiPageWikiLink Irrational_number.
- Angle_trisection wikiPageWikiLink Irreducible_polynomial.
- Angle_trisection wikiPageWikiLink Isosceles_triangle.
- Angle_trisection wikiPageWikiLink Limacon.
- Angle_trisection wikiPageWikiLink Limaçon.
- Angle_trisection wikiPageWikiLink Line_(geometry).
- Angle_trisection wikiPageWikiLink Line_(mathematics).
- Angle_trisection wikiPageWikiLink List_of_geometry_topics.
- Angle_trisection wikiPageWikiLink List_of_trigonometric_identities.
- Angle_trisection wikiPageWikiLink Logical_consequence.
- Angle_trisection wikiPageWikiLink Mathematical_proof.
- Angle_trisection wikiPageWikiLink Mathematics_Teacher.
- Angle_trisection wikiPageWikiLink Minimal_polynomial_(field_theory).
- Angle_trisection wikiPageWikiLink Morleys_trisector_theorem.
- Angle_trisection wikiPageWikiLink National_Council_of_Teachers_of_Mathematics.
- Angle_trisection wikiPageWikiLink Natural_number.
- Angle_trisection wikiPageWikiLink Neusis_construction.
- Angle_trisection wikiPageWikiLink Nicomedes_(mathematician).
- Angle_trisection wikiPageWikiLink Origami.
- Angle_trisection wikiPageWikiLink Parallel_(geometry).
- Angle_trisection wikiPageWikiLink Pierre_Wantzel.
- Angle_trisection wikiPageWikiLink Polygon.
- Angle_trisection wikiPageWikiLink Polynomial.
- Angle_trisection wikiPageWikiLink Pons_asinorum.
- Angle_trisection wikiPageWikiLink Positive_integer.
- Angle_trisection wikiPageWikiLink Prime_number.
- Angle_trisection wikiPageWikiLink Proof_of_impossibility.
- Angle_trisection wikiPageWikiLink Pseudomathematics.
- Angle_trisection wikiPageWikiLink Q.E.D..
- Angle_trisection wikiPageWikiLink Quadratrix.
- Angle_trisection wikiPageWikiLink Radian.
- Angle_trisection wikiPageWikiLink Radius.
- Angle_trisection wikiPageWikiLink Rational_number.
- Angle_trisection wikiPageWikiLink Rational_numbers.
- Angle_trisection wikiPageWikiLink Rational_root.
- Angle_trisection wikiPageWikiLink Rational_root_theorem.
- Angle_trisection wikiPageWikiLink Ray_(geometry).
- Angle_trisection wikiPageWikiLink Right_angle.
- Angle_trisection wikiPageWikiLink Square.
- Angle_trisection wikiPageWikiLink Square_(geometry).
- Angle_trisection wikiPageWikiLink Squaring_the_circle.
- Angle_trisection wikiPageWikiLink Steel_square.
- Angle_trisection wikiPageWikiLink Straightedge.