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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.
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 ]
In general, the same inversion transforms the given circle C 1 and C 2 into two new circles, c 1 and c 2. Thus, the problem becomes that of finding a solution line tangent to the two inverted circles, which was solved above. There are four such lines, and re-inversion transforms them into the four solution circles of the original Apollonius ...
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.
Gergonne's approach is to consider the solution circles in pairs. [1] Let a pair of solution circles be denoted as C A and C B (the pink circles in Figure 6), and let their tangent points with the three given circles be denoted as A 1, A 2, A 3, and B 1, B 2, B 3, respectively. Gergonne's solution aims to locate these six points, and thus solve ...
Packing of irregular objects is a problem not lending itself well to closed form solutions; however, the applicability to practical environmental science is quite important. For example, irregularly shaped soil particles pack differently as the sizes and shapes vary, leading to important outcomes for plant species to adapt root formations and ...
Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack n unit circles into the smallest possible square. Equivalently, the problem is to arrange n points in a unit square aiming to get the greatest minimal separation, d n , between points. [ 1 ]