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  2. Inversive geometry - Wikipedia

    en.wikipedia.org/wiki/Inversive_geometry

    In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves. Many difficult problems in geometry become much more tractable when an inversion is applied.

  3. Inverse curve - Wikipedia

    en.wikipedia.org/wiki/Inverse_curve

    In inversive geometry, an inverse curve of a given curve C is the result of applying an inverse operation to C. Specifically, with respect to a fixed circle with center O and radius k the inverse of a point Q is the point P for which P lies on the ray OQ and OP·OQ = k 2. The inverse of the curve C is then the locus of P as Q runs over C.

  4. Plane-based geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Plane-based_geometric_algebra

    Inversive geometry itself can be performed with the larger system known as Conformal Geometric Algebra(CGA), of which Plane-based GA is a subalgebra. CGA is also usually applied to 3D space, and is able to model general spheres, circles, and conformal (angle-preserving) transformations, which include the transformations seen on the Poincare ...

  5. Category:Unsolved problems in geometry - Wikipedia

    en.wikipedia.org/wiki/Category:Unsolved_problems...

    Download as PDF; Printable version; In other projects Wikidata item; ... Help. Pages in category "Unsolved problems in geometry" The following 48 pages are in this ...

  6. 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.

  7. Category:Inversive geometry - Wikipedia

    en.wikipedia.org/wiki/Category:Inversive_geometry

    Download as PDF; Printable version; In other projects ... Appearance. move to sidebar hide. Help. Pages in category "Inversive geometry" The following 13 pages are in ...

  8. Problem of Apollonius - Wikipedia

    en.wikipedia.org/wiki/Problem_of_Apollonius

    A natural setting for problem of Apollonius is inversive geometry. [4] [12] The basic strategy of inversive methods is to transform a given Apollonius problem into another Apollonius problem that is simpler to solve; the solutions to the original problem are found from the solutions of the transformed problem by undoing the transformation ...

  9. Moser's worm problem - Wikipedia

    en.wikipedia.org/wiki/Moser's_worm_problem

    Moser's worm problem (also known as mother worm's blanket problem) is an unsolved problem in geometry formulated by the Austrian-Canadian mathematician Leo Moser in 1966. The problem asks for the region of smallest area that can accommodate every plane curve of length 1.

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