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A compact binary circle packing with the most similarly sized circles possible. [7] It is also the densest possible packing of discs with this size ratio (ratio of 0.6375559772 with packing fraction (area density) of 0.910683). [8] There are also a range of problems which permit the sizes of the circles to be non-uniform.
Each circle is tangent to the base line and its neighboring circles. Irreducible fractions with the same denominator have circles of the same size. In mathematics, a Ford circle is a circle in the Euclidean plane, in a family of circles that are all tangent to the -axis at rational points.
In geometry, unit fractions can be used to characterize the curvature of triangle groups and the tangencies of Ford circles. Unit fractions are commonly used in fair division , and this familiar application is used in mathematics education as an early step toward the understanding of other fractions.
For every fraction p / q (in its lowest terms) there is a Ford circle C[p/q], which is the circle with radius and centre at (,). Two Ford circles for different fractions are either disjoint or they are tangent to one another—two Ford circles never intersect.
A circle bounds a region of the plane called a disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern
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 ]