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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.
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that
Circle packing in a circle is a two-dimensional packing problem with the objective of packing unit circles into the smallest possible larger circle. Table of solutions, 1 ≤ n ≤ 20 [ edit ]
The solution of the problem of squaring the circle by compass and straightedge requires the construction of the number , the length of the side of a square whose area equals that of a unit circle. If π {\displaystyle {\sqrt {\pi }}} were a constructible number , it would follow from standard compass and straightedge constructions that π ...
These two circles determine a pencil, meaning a line L in the P 3 of circles. If the equations of C 0 and C ∞ are f and g, respectively, then the points on L correspond to the circles whose equations are Sf + Tg, where [S : T] is a point of P 1. The points where L meets Z D are precisely the circles in the pencil that are tangent to D.
Packing circles in simple bounded shapes is a common type of problem in recreational mathematics. The influence of the container walls is important, and hexagonal packing is generally not optimal for small numbers of circles. Specific problems of this type that have been studied include: Circle packing in a circle; Circle packing in a square
There are four such circles in general, the inscribed circle of the triangle formed by the intersection of the three lines, and the three exscribed circles. A general Apollonius problem can be transformed into the simpler problem of circle tangent to one circle and two parallel lines (itself a special case of the LLC special case).
The smallest-circle problem (also known as minimum covering circle problem, bounding circle problem, least bounding circle problem, smallest enclosing circle problem) is a computational geometry problem of computing the smallest circle that contains all of a given set of points in the Euclidean plane.
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