Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Doubling_the_cube> ?p ?o }
- Doubling_the_cube abstract "Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first, using only the tools of a compass and straightedge. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be impossible.The Egyptians, Indians, and particularly the Greeks were aware of the problem and made many futile attempts at solving what they saw as an obstinate but soluble problem. However, the nonexistence of a solution was finally proven by Pierre Wantzel in 1837, applying the recent development of abstract algebra by Galois.In algebraic terms, doubling a unit cube requires the construction of a line segment of length x, where x3 = 2; in other words, x = 3√2. This is because a cube of side length 1 has a volume of 13 = 1, and a cube of twice that volume (a volume of 2) has a side length of the cube root of 2. The impossibility of doubling the cube is therefore equivalent to the statement that 3√2 is not a constructible number. This is a consequence of the fact that the coordinates of a new point constructed by a compass and straightedge are roots of polynomials over the field generated by the coordinates of previous points, of no greater degree than a quadratic. This implies that the degree of the field generated by a constructible point must be a power of 2. The field generated by 3√2, however, is of degree 3.".
- Doubling_the_cube wikiPageExternalLink section80.
- Doubling_the_cube wikiPageExternalLink cubedbl.htm.
- Doubling_the_cube wikiPageExternalLink Doubling_the_cube.html.
- Doubling_the_cube wikiPageExternalLink Delian.shtml.
- Doubling_the_cube wikiPageID "91110".
- Doubling_the_cube wikiPageLength "11472".
- Doubling_the_cube wikiPageOutDegree "83".
- Doubling_the_cube wikiPageRevisionID "681183493".
- Doubling_the_cube wikiPageWikiLink Abstract_algebra.
- Doubling_the_cube wikiPageWikiLink Analytic_geometry.
- Doubling_the_cube wikiPageWikiLink Ancient_Egyptian_mathematics.
- Doubling_the_cube wikiPageWikiLink Angle_trisection.
- Doubling_the_cube wikiPageWikiLink Apollo.
- Doubling_the_cube wikiPageWikiLink Archytas.
- Doubling_the_cube wikiPageWikiLink Cartesian_coordinate_system.
- Doubling_the_cube wikiPageWikiLink Cartesian_plane.
- Doubling_the_cube wikiPageWikiLink Category:Compass_and_straightedge_constructions.
- Doubling_the_cube wikiPageWikiLink Category:Euclidean_plane_geometry.
- Doubling_the_cube wikiPageWikiLink Category:History_of_geometry.
- Doubling_the_cube wikiPageWikiLink Category:Mathematical_problems.
- Doubling_the_cube wikiPageWikiLink Centre_(geometry).
- Doubling_the_cube wikiPageWikiLink Circle.
- Doubling_the_cube wikiPageWikiLink Circles.
- Doubling_the_cube wikiPageWikiLink Cissoid_of_Diocles.
- Doubling_the_cube wikiPageWikiLink Coefficient.
- Doubling_the_cube wikiPageWikiLink Coefficients.
- Doubling_the_cube wikiPageWikiLink Compass-and-straightedge_construction.
- Doubling_the_cube wikiPageWikiLink Compass_and_straightedge.
- Doubling_the_cube wikiPageWikiLink Conchoid_(mathematics).
- Doubling_the_cube wikiPageWikiLink Conic.
- Doubling_the_cube wikiPageWikiLink Conic_section.
- Doubling_the_cube wikiPageWikiLink Constructible_number.
- Doubling_the_cube wikiPageWikiLink Coordinate.
- Doubling_the_cube wikiPageWikiLink Coordinate_system.
- Doubling_the_cube wikiPageWikiLink Crank_(person).
- Doubling_the_cube wikiPageWikiLink Cube.
- Doubling_the_cube wikiPageWikiLink Cube_root.
- Doubling_the_cube wikiPageWikiLink Cut-the-Knot.
- Doubling_the_cube wikiPageWikiLink Cut-the-knot.
- Doubling_the_cube wikiPageWikiLink Degree_of_a_field_extension.
- Doubling_the_cube wikiPageWikiLink Degree_of_a_polynomial.
- Doubling_the_cube wikiPageWikiLink Delos.
- Doubling_the_cube wikiPageWikiLink Delphi.
- Doubling_the_cube wikiPageWikiLink Edge_(geometry).
- Doubling_the_cube wikiPageWikiLink Egyptian_mathematics.
- Doubling_the_cube wikiPageWikiLink Eratosthenes.
- Doubling_the_cube wikiPageWikiLink Eudoxus_of_Cnidus.
- Doubling_the_cube wikiPageWikiLink Eutocius_of_Ascalon.
- Doubling_the_cube wikiPageWikiLink Factorisation.
- Doubling_the_cube wikiPageWikiLink Factorization.
- Doubling_the_cube wikiPageWikiLink Field_(mathematics).
- Doubling_the_cube wikiPageWikiLink Field_extension.
- Doubling_the_cube wikiPageWikiLink Galois.
- Doubling_the_cube wikiPageWikiLink Gausss_lemma_(polynomial).
- Doubling_the_cube wikiPageWikiLink Geometry.
- Doubling_the_cube wikiPageWikiLink Greek_mathematics.
- Doubling_the_cube wikiPageWikiLink Hippocrates_of_Chios.
- Doubling_the_cube wikiPageWikiLink Indian_mathematics.
- Doubling_the_cube wikiPageWikiLink Integer.
- Doubling_the_cube wikiPageWikiLink Intersection.
- Doubling_the_cube wikiPageWikiLink Irreducible_polynomial.
- Doubling_the_cube wikiPageWikiLink Line_segment.
- Doubling_the_cube wikiPageWikiLink Linear_factor.
- Doubling_the_cube wikiPageWikiLink Linear_function.
- Doubling_the_cube wikiPageWikiLink Logical_equivalence.
- Doubling_the_cube wikiPageWikiLink Mathematical_induction.
- Doubling_the_cube wikiPageWikiLink Mathematics.
- Doubling_the_cube wikiPageWikiLink Mathematics_of_origami.
- Doubling_the_cube wikiPageWikiLink Mathematics_of_paper_folding.
- Doubling_the_cube wikiPageWikiLink Menaechmus.
- Doubling_the_cube wikiPageWikiLink Minimal_polynomial_(field_theory).
- Doubling_the_cube wikiPageWikiLink Neusis_construction.
- Doubling_the_cube wikiPageWikiLink Oracle.
- Doubling_the_cube wikiPageWikiLink Origin_(mathematics).
- Doubling_the_cube wikiPageWikiLink Parallel_(geometry).
- Doubling_the_cube wikiPageWikiLink Philo_line.
- Doubling_the_cube wikiPageWikiLink Pierre_Wantzel.
- Doubling_the_cube wikiPageWikiLink Plato.
- Doubling_the_cube wikiPageWikiLink Plutarch.
- Doubling_the_cube wikiPageWikiLink Polynomial.
- Doubling_the_cube wikiPageWikiLink Power_of_2.
- Doubling_the_cube wikiPageWikiLink Power_of_two.
- Doubling_the_cube wikiPageWikiLink Pseudomathematics.
- Doubling_the_cube wikiPageWikiLink Pure_geometry.
- Doubling_the_cube wikiPageWikiLink Quadratic_function.
- Doubling_the_cube wikiPageWikiLink Quadratic_polynomial.
- Doubling_the_cube wikiPageWikiLink Rational_number.
- Doubling_the_cube wikiPageWikiLink Rational_numbers.
- Doubling_the_cube wikiPageWikiLink Real_number.
- Doubling_the_cube wikiPageWikiLink Real_numbers.
- Doubling_the_cube wikiPageWikiLink Sisyphus_(dialogue).
- Doubling_the_cube wikiPageWikiLink Squaring_the_circle.
- Doubling_the_cube wikiPageWikiLink Straightedge_and_compass.
- Doubling_the_cube wikiPageWikiLink Synthetic_geometry.
- Doubling_the_cube wikiPageWikiLink Trisecting_the_angle.
- Doubling_the_cube wikiPageWikiLink Unit_cube.
- Doubling_the_cube wikiPageWikiLink Volume.
- Doubling_the_cube wikiPageWikiLink Évariste_Galois.
- Doubling_the_cube wikiPageWikiLink File:Doubling_the_cube.svg.