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  2. Parallelogram of force - Wikipedia

    en.wikipedia.org/wiki/Parallelogram_of_force

    When more than two forces are involved, the geometry is no longer a parallelogram, but the same principles apply to a polygon of forces. The resultant force due to the application of a number of forces can be found geometrically by drawing arrows for each force. The parallelogram of forces is a graphical manifestation of the addition of vectors.

  3. Parametrization (geometry) - Wikipedia

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

    In mathematics, and more specifically in geometry, parametrization (or parameterization; also parameterisation, parametrisation) is the process of finding parametric equations of a curve, a surface, or, more generally, a manifold or a variety, defined by an implicit equation.

  4. Parallelogram law - Wikipedia

    en.wikipedia.org/wiki/Parallelogram_law

    Vectors involved in the parallelogram law. In a normed space, the statement of the parallelogram law is an equation relating norms: ‖ ‖ + ‖ ‖ = ‖ + ‖ + ‖ ‖,.. The parallelogram law is equivalent to the seemingly weaker statement: ‖ ‖ + ‖ ‖ ‖ + ‖ + ‖ ‖, because the reverse inequality can be obtained from it by substituting (+) for , and () for , and then simplifying.

  5. Varignon's theorem - Wikipedia

    en.wikipedia.org/wiki/Varignon's_theorem

    The Varignon parallelogram is a rectangle if and only if the diagonals of the quadrilateral are perpendicular, that is, if the quadrilateral is an orthodiagonal quadrilateral. [6]: p. 14 [7]: p. 169 For a self-crossing quadrilateral, the Varignon parallelogram can degenerate to four collinear points, forming a line segment traversed twice.

  6. Mathematical problem - Wikipedia

    en.wikipedia.org/wiki/Mathematical_problem

    Known as word problems, they are used in mathematics education to teach students to connect real-world situations to the abstract language of mathematics. In general, to use mathematics for solving a real-world problem, the first step is to construct a mathematical model of the problem. This involves abstraction from the details of the problem ...

  7. Equipollence (geometry) - Wikipedia

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

    A property of Euclidean spaces is the parallelogram property of vectors: If two segments are equipollent, then they form two sides of a parallelogram: If a given vector holds between a and b, c and d, then the vector which holds between a and c is the same as that which holds between b and d.

  8. Cyclic quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Cyclic_quadrilateral

    Examples of cyclic quadrilaterals. In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic.

  9. List of unsolved problems in mathematics - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.