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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.
CLP problems generally have 4 solutions. The solution of this special case is similar to that of the CPP Apollonius solution. Draw a circle centered on the given point P; since the solution circle must pass through P, inversion in this [clarification needed] circle transforms the solution circle
Consider a solution circle of radius r s and three given circles of radii r 1, r 2 and r 3. If the solution circle is externally tangent to all three given circles, the distances between the center of the solution circle and the centers of the given circles equal d 1 = r 1 + r s, d 2 = r 2 + r s and d 3 = r 3 + r s, respectively.
We know which of the points P i defining Q j is closer to the each point of the halfline containing center of the enclosing circle of the constrained problem solution. This point could be discarded. The half-plane where the unconstrained solution lies could be determined by the points P i on the boundary of the constrained circle solution. (The ...
A circle (C 3) centered at B' with radius |B'B| meets the circle (C 2) at A'. A circle (C 4) centered at A' with radius |A'A| meets the circle (C 1) at E and E'. Two circles (C 5) centered at E and (C 6) centered at E' with radius |EA| meet at A and O. O is the sought center of |AD|. The design principle can also be applied to a line segment AD.
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The solutions to this problem are sometimes called the circles of Apollonius. The Apollonian gasket —one of the first fractals ever described—is a set of mutually tangent circles, formed by solving Apollonius' problem iteratively.