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The chain closes, in the sense that the sixth circle is always tangent to the first circle. [1] [2] It is assumed in this construction that all circles lie within the triangle, and all points of tangency lie on the sides of the triangle. If the problem is generalized to allow circles that may not be within the triangle, and points of tangency ...
Five circles theorem – Derives a pentagram from five chained circles centered on a common sixth circle; Gauss circle problem – How many integer lattice points there are in a circle; Gershgorin circle theorem – Bound on eigenvalues; Geometrography – Study of geometrical constructions
This problem is known as the primitive circle problem, as it involves searching for primitive solutions to the original circle problem. [9] It can be intuitively understood as the question of how many trees within a distance of r are visible in the Euclid's orchard , standing in the origin.
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
The second theorem considers five circles in general position passing through a single point M. Each subset of four circles defines a new point P according to the first theorem. Then these five points all lie on a single circle C. The third theorem considers six circles in general position that pass through a single point M. Each subset of five ...
Pages for logged out editors learn more. Contributions; ... Print/export Download as PDF; ... Pages in category "Theorems about circles"
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