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...solved [[conjecture]] of [[Hugo Hadwiger]] that every [[simplex]] can be [[Dissection problem|dissected]] into [[Schläfli orthoscheme|orthoscheme]]s, using a num [[File:Triangulated cube.svg|thumb|upright=1.5|Dissection of a cube into six orthoschemes]] ...

...d the two line segments it creates on the hypotenuse. It states that the [[geometric mean]] of those two segments equals the altitude. [[File:Sehnensatz hoehensatz.svg|thumb|upright=1.2|geometric mean theorem as a special case of the [[intersecting chords theorem]]:<br/> ...

{{Short description|3D geometric shape}} == Dissection== ...

...r's paradox''' is a [[falsidical paradox]] based on an optical illusion. A geometric shape with an area of 32 units is dissected into four parts, which afterwar ...cted in the 1782 edition. However Hooper was not the first to publish this geometric fallacy, since Hooper's book was largely an adaption of [[Edmé-Gilles Guyot ...

[[File:Schachbrett paradox allgemein fib2.svg|thumb|upright=1.5|Generalised dissection of a square using Fibonacci numbers]] [[File:Schachbrett paradox allgemein fib3.svg|thumb|upright=1.5|Dissection without an area mismatch <math>\varphi=\frac{1+\sqrt{5}}{2} </math>]] ...

...n''-dissection, and it is classified as an ''even dissection'' or an ''odd dissection'' according to whether ''n'' is [[Parity (mathematics)|even or odd]].{{sfn| An ''equidissection'' is a dissection in which every triangle has the same area. For a polygon ''P'', the set of ...

| title = A color-matching dissection of the rhombic enneacontahedron | title = Twelve geometric essays ...

....<ref>[https://scilogs.fr/complexites/pepites-geometriques-cachees/ Hidden geometric nuggets] by Jean-Paul Delahaye, by Jean-Paul Delahaye, 04-07-2013</ref> A ...ref>[http://www.maa.org/publications/maa-reviews/geometric-magic-squares ''Geometric Magic Squares'' reviewed by Charles Ashbacher] [[Mathematical Association o ...

...Antu built geometrical models based on a major arc of a circle and the nth dissection of the major arc. In Fig 1, ''AE'' is the major chord of arc ''ABCDE'', and [[File:Geyuanmilu2.jpg|thumb|400px|Fig. 2: Ming Antu's geometric model of 2-segment chord]] ...

...oblems on these graphs. Separator hierarchies may also be used in [[nested dissection]], an efficient variant of [[Gaussian elimination]] for solving [[sparse ma ...that it provides an improved constant factor in the time bounds for nested dissection compared to the separators of {{harvtxt|Alon|Seymour|Thomas|1990}}. The siz ...

...ets of the theory. In fact, the concept of valuation has its origin in the dissection theory of [[polytope]]s and in particular [[Hilbert's third problem]], whic ...uct of <math>C^2(S^{n-1}),</math> the latter space of functions having the geometric meaning of differences of support functions of smooth convex bodies. For de ...

...ny mathematical theorem. The proofs are diverse, including both [[Geometry|geometric]] proofs and [[Algebra|algebraic]] proofs, with some dating back thousands ...agoras contains no statement specifying this or any other particular great geometric discovery to him."<ref>{{harvtxt|Euclid|1956}}, pp. 351–352</ref> Recent s ...

...ing|shearing]] and [[Rotation (mathematics)|rotating]] triangles. In the ''dissection proof'', the square of the hypotenuse is cut into pieces to fit into the ot ...century, [[formulas]] were discovered to calculate pi without the need for geometric diagrams. These formulas used infinite series and [[trigonometric functions ...

{{Short description|Geometric theorem}} ...is a [[paradox#Veridical_paradox|veridical paradox]]: it contradicts basic geometric intuition, but is not false or self-contradictory. "Doubling the ball" by d ...

Fuller's geometric explorations provide an experiential basis for designing and refining a phi His modular dissection of a space-filling tetrahedron or MITE (minimum tetrahedron) into 2 A and 1 ...