Մասնակից:Nagolil/Ավազարկղ
From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Mathematical_proof
https://en.wikipedia.org/wiki/Parallel_postulate
https://en.wikipedia.org/wiki/G%C3%BCnter_M._Ziegler
https://en.wikipedia.org/wiki/Internal_and_external_angles
https://en.wikipedia.org/wiki/Karl_Georg_Christian_von_Staudt
https://en.wikipedia.org/wiki/Carl_Anton_Bretschneider
https://en.wikipedia.org/wiki/Christoph_Grienberger
https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol
Լիլո նայի
- https://en.wikipedia.org/wiki/Polygonal_chain
- https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%91%D0%B0%D0%BB%D0%B8%D0%BD%D1%81%D0%BA%D0%BE%D0%B3%D0%BE
- https://en.wikipedia.org/wiki/Distance
- https://en.wikipedia.org/wiki/Vertex_(geometry)
- https://en.wikipedia.org/wiki/Vertex_(graph_theory)
- https://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle
- https://en.wikipedia.org/wiki/Circumconic_and_inconic
- https://en.wikipedia.org/wiki/Face_(geometry)
- https://en.wikipedia.org/wiki/K-vertex-connected_graph
- https://en.wikipedia.org/wiki/Tesseract
- https://en.wikipedia.org/wiki/Trilinear_coordinates
- https://en.wikipedia.org/wiki/Barycentric_coordinate_system
- https://en.wikipedia.org/wiki/Ex-tangential_quadrilateral
- https://en.wikipedia.org/wiki/Bisection
- https://en.wikipedia.org/wiki/N-skeleton
- https://en.wikipedia.org/wiki/Acute_and_obtuse_triangles
- https://en.wikipedia.org/wiki/Inellipse
- https://en.wikipedia.org/wiki/Centroid
- https://en.wikipedia.org/wiki/Congruence_(geometry)
- https://en.wikipedia.org/wiki/Concentric_spheres
- https://en.wikipedia.org/wiki/Uniform_polyhedron
- https://en.wikipedia.org/wiki/Quasiregular_polyhedron
- https://en.wikipedia.org/wiki/Two-dimensional_space
- https://en.wikipedia.org/wiki/Circumscribed_circle
- https://en.wikipedia.org/wiki/Chamfer_(geometry)
- https://en.wikipedia.org/wiki/Dual_polyhedron
- https://en.wikipedia.org/wiki/Unit_sphere
- https://en.wikipedia.org/wiki/Kite_(geometry)
- https://en.wikipedia.org/wiki/Configuration_(polytope)#Higher_dimensions
- https://en.wikipedia.org/wiki/Angular_defect
- https://en.wikipedia.org/wiki/Peano_axioms
- https://en.wikipedia.org/wiki/Regular_polytope
- https://en.wikipedia.org/wiki/Convex_set
- https://en.wikipedia.org/wiki/Octahedron
- https://en.wikipedia.org/wiki/Regular_dodecahedron
- https://en.wikipedia.org/wiki/List_of_regular_polytopes_and_compounds
- https://en.wikipedia.org/wiki/Regular_icosahedron
- https://en.wikipedia.org/wiki/Tetrahedron
- https://en.wikipedia.org/wiki/Functional_analysis
- https://en.wikipedia.org/wiki/Theorem
- https://en.wikipedia.org/wiki/Norm_(mathematics)
- https://ru.wikipedia.org/wiki/%D0%9F%D0%BE%D0%BB%D1%83%D0%BD%D0%BE%D1%80%D0%BC%D0%B0
- https://en.wikipedia.org/wiki/Normed_vector_space
- https://en.wikipedia.org/wiki/Sine
- https://en.wikipedia.org/wiki/Butterfly_theorem
- https://en.wikipedia.org/wiki/Secant_line
- https://en.wikipedia.org/wiki/Chord_(geometry)
- https://en.wikipedia.org/wiki/Robbins_pentagon
- https://en.wikipedia.org/wiki/Casey%27s_theorem
- https://en.wikipedia.org/wiki/Ptolemaic_graph
- https://en.wikipedia.org/wiki/Central_angle
- https://en.wikipedia.org/wiki/Circumference
- https://en.wikipedia.org/wiki/Inscribed_figure
- https://en.wikipedia.org/wiki/Cycle_(graph_theory)
- https://en.wikipedia.org/wiki/Concentric_objects
- https://ru.wikipedia.org/wiki/%D0%9A%D1%80%D0%B8%D0%B2%D0%B0%D1%8F_%D0%B2%D1%82%D0%BE%D1%80%D0%BE%D0%B3%D0%BE_%D0%BF%D0%BE%D1%80%D1%8F%D0%B4%D0%BA%D0%B0
- https://en.wikipedia.org/wiki/Ptolemy%27s_table_of_chords
- https://ru.wikipedia.org/wiki/Sgn
- https://en.wikipedia.org/wiki/Power_of_a_point
- https://en.wikipedia.org/wiki/Inscribed_angle
- https://en.wikipedia.org/wiki/Collinearity
- https://en.wikipedia.org/wiki/Arc_length
- https://en.wikipedia.org/wiki/Asteroseismology
- https://en.wikipedia.org/wiki/Helioseismology
- https://en.wikipedia.org/wiki/Marsquake
նյութը
Բարելավելու ենթակա
- https://en.wikipedia.org/wiki/Trigonometry
- https://en.wikipedia.org/wiki/Area
- https://en.wikipedia.org/wiki/Logarithm
- https://en.wikipedia.org/wiki/Pi
- https://en.wikipedia.org/wiki/Differential_equation
- https://en.wikipedia.org/wiki/Numerical_analysis
- https://en.wikipedia.org/wiki/Infinity
- https://en.wikipedia.org/wiki/Function_(mathematics)
- https://en.wikipedia.org/wiki/Academy_Award_for_Best_Actress
- https://en.wikipedia.org/wiki/God
- https://en.wikipedia.org/wiki/Eve
- https://en.wikipedia.org/wiki/Flood_myth
- https://en.wikipedia.org/wiki/Delta_(letter)
- https://en.wikipedia.org/wiki/Abacus_(architecture)
- https://en.wikipedia.org/wiki/Palazzo_Pitti
- https://en.wikipedia.org/wiki/Kinetic_energy
- https://en.wikipedia.org/wiki/Engineering_drawing
- https://en.wikipedia.org/wiki/Level_(instrument)
- https://en.wikipedia.org/wiki/Crosier
- https://en.wikipedia.org/wiki/Aesop
- https://en.wikipedia.org/wiki/Water
- https://en.wikipedia.org/wiki/Pearl
- https://en.wikipedia.org/wiki/Earthquake
- https://en.wikipedia.org/wiki/Line_segment
- https://en.wikipedia.org/wiki/Parallel_(geometry)
Многогранник, двойственный (или дуальный) к заданному многограннику — многогранник, у которого каждой грани исходного многогранника соответствует вершина двойственного, каждой вершине исходного — грань двойственного. Количество рёбер исходного и двойственного многогранника одинаково. Многогранник, двойственный двойственному, гомотетичен исходному.
In geometry, any polyhedron is associated with a second dual figure, where the vertices of one correspond to the faces of the other and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other.[1] Such dual figures remain combinatorial or abstract polyhedra, but not all are also geometric polyhedra.[2] Starting with any given polyhedron, the dual of its dual is the original polyhedron.
Duality preserves the symmetries of a polyhedron. Therefore, for many classes of polyhedra defined by their symmetries, the duals also belong to a symmetric class. Thus, the regular polyhedra – the (convex) Platonic solids and (star) Kepler–Poinsot polyhedra – form dual pairs, where the regular tetrahedron is self-dual. The dual of an isogonal polyhedron, having equivalent vertices, is one which is isohedral, having equivalent faces. The dual of an isotoxal polyhedron (having equivalent edges) is also isotoxal.
Duality is closely related to reciprocity or polarity, a geometric transformation that, when applied to a convex polyhedron, realizes the dual polyhedron as another convex polyhedron.
В геометрии любой многогранник связан со второй двойной фигурой, где вершины одного соответствуют граням другого, а ребра между парами вершин одного соответствуют ребрам между парами граней другого. [1] Такие двойные фигуры остаются комбинаторными или абстрактными многогранниками, но не все они также являются геометрическими многогранниками. [2] Начиная с любого заданного многогранника, двойственный его двойственный является исходным многогранником.
Двойственность сохраняет симметрии многогранника. Следовательно, для многих классов многогранников, определяемых их симметриями, дуалы также принадлежат к симметрическому классу. Таким образом, правильные многогранники - (выпуклые) твердые тела Платона и (звездные) многогранники Кеплера – Пуансо - образуют двойственные пары, где правильный тетраэдр самодуален. Двойственный изогональный многогранник, имеющий эквивалентные вершины, является изоэдральным, имеющим эквивалентные грани. Двойственный изотоксальный многогранник (имеющий эквивалентные ребра) также изотоксален.
Двойственность тесно связана с взаимностью или полярностью, геометрическим преобразованием, которое при применении к выпуклому многограннику реализует двойной многогранник как другой выпуклый многогранник.