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  2. Van Hiele model - Wikipedia

    en.wikipedia.org/wiki/Van_Hiele_model

    The model has greatly influenced geometry curricula throughout the world through emphasis on analyzing properties and classification of shapes at early grade levels. In the United States, the theory has influenced the geometry strand of the Standards published by the National Council of Teachers of Mathematics and the Common Core Standards.

  3. Algebraic geometry - Wikipedia

    en.wikipedia.org/wiki/Algebraic_geometry

    Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects.

  4. Mathematics - Wikipedia

    en.wikipedia.org/wiki/Mathematics

    Algebra (and later, calculus) can thus be used to solve geometrical problems. Geometry was split into two new subfields: synthetic geometry, which uses purely geometrical methods, and analytic geometry, which uses coordinates systemically. [23] Analytic geometry allows the study of curves unrelated to circles and lines.

  5. Foundations of geometry - Wikipedia

    en.wikipedia.org/wiki/Foundations_of_geometry

    Absolute geometry is a geometry based on an axiom system consisting of all the axioms giving Euclidean geometry except for the parallel postulate or any of its alternatives. [69] The term was introduced by János Bolyai in 1832. [70] It is sometimes referred to as neutral geometry, [71] as it is neutral with respect to the parallel postulate.

  6. Similarity (geometry) - Wikipedia

    en.wikipedia.org/wiki/Similarity_(geometry)

    Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.

  7. Geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Geometric_algebra

    A multivector that is the exterior product of linearly independent vectors is called a blade, and is said to be of grade ⁠ ⁠. [f] A multivector that is the sum of blades of grade is called a (homogeneous) multivector of grade ⁠ ⁠. From the axioms, with closure, every multivector of the geometric algebra is a sum of blades.

  8. 10-simplex - Wikipedia

    en.wikipedia.org/wiki/10-simplex

    In geometry, a 10-simplex is a self-dual regular 10-polytope. It has 11 vertices , 55 edges , 165 triangle faces , 330 tetrahedral cells , 462 5-cell 4-faces, 462 5-simplex 5-faces, 330 6-simplex 6-faces, 165 7-simplex 7-faces, 55 8-simplex 8-faces, and 11 9-simplex 9-faces.

  9. Hilbert's tenth problem - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_tenth_problem

    Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900. It is the challenge to provide a general algorithm that, for any given Diophantine equation (a polynomial equation with integer coefficients and a finite number of unknowns), can decide whether the equation has a solution with all unknowns taking integer values.

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