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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.
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 subproblem is either the solution of the unconstrained problem or it is used to determine the half-plane where the unconstrained solution center is located. The n 16 {\textstyle {\frac {n}{16}}} points to be discarded are found as follows: The points P i are arranged into pairs which defines n 2 {\textstyle {\frac {n}{2 ...
For example, a circular disk of radius 1/2 can accommodate any plane curve of length 1 by placing the midpoint of the curve at the center of the disk. Another possible solution has the shape of a rhombus with vertex angles of 60° and 120° and with a long diagonal of unit length. [ 2 ]
Levi, Mark (2009), "6.3 How Much Gold Is in a Wedding Ring?", The Mathematical Mechanic: Using Physical Reasoning to Solve Problems, Princeton University Press, pp. 102– 104, ISBN 978-0-691-14020-9. Levi argues that the volume depends only on the height of the hole based on the fact that the ring can be swept out by a half-disk with the ...
For the problem as originally stated, =, = / and = /, which gives = (). This is a vast timespan, even compared to the estimated age of the universe , which is only about 4 × 10 17 s . Furthermore, the length of the rope after such a time is similarly huge, 2.8 × 10 43 429 km, so it is only in a mathematical sense that the ant can ever reach ...
The goat problems do not yield any new mathematical insights; rather they are primarily exercises in how to artfully deconstruct problems in order to facilitate solution. Three-dimensional analogues and planar boundary/area problems on other shapes, including the obvious rectangular barn and/or field, have been proposed and solved. [ 1 ]
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.
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