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In the example in the figure, the following 4 × 4 most-perfect magic square was copied into the upper part of the magic circle. Each number, with 16 added, was placed at the intersection symmetric about the centre of the circles. This results in a magic circle containing numbers 1 to 32, with each circle and diameter totalling 132. [1]
In geometry, a set of Johnson circles comprises three circles of equal radius r sharing one common point of intersection H.In such a configuration the circles usually have a total of four intersections (points where at least two of them meet): the common point H that they all share, and for each of the three pairs of circles one more intersection point (referred here as their 2-wise intersection).
The radical axis of a pair of circles is defined as the set of points that have equal power h with respect to both circles. For example, for every point P on the radical axis of circles 1 and 2, the powers to each circle are equal: h 1 = h 2. Similarly, for every point on the radical axis of circles 2 and 3, the powers must be equal, h 2 = h 3.
Fifteen equal circles packed within the smallest possible square. Only four equilateral triangles are formed by adjacent circles. 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 ...
Each of the Archimedes' quadruplets (green) have equal area to each other and to Archimedes' twin circles. In geometry, Archimedes' quadruplets are four congruent circles associated with an arbelos. Introduced by Frank Power in the summer of 1998, each have the same area as Archimedes' twin circles, making them Archimedean circles. [1] [2] [3]
0, 4, 8, 16, 32, 48, 72, 88, 120, 152, 192 … (sequence A175341 in the OEIS ). Using the same ideas as the usual Gauss circle problem and the fact that the probability that two integers are coprime is 6 / π 2 {\displaystyle 6/\pi ^{2}} , it is relatively straightforward to show that
gcd(m, n) (greatest common divisor of m and n) is the product of all prime factors which are both in m and n (with the smallest multiplicity for m and n). m and n are coprime (also called relatively prime) if gcd( m , n ) = 1 (meaning they have no common prime factor).
The simplest Brunnian link other than the 6-crossing Borromean rings is presumably the 10-crossing L10a140 link. [1]An example of an n-component Brunnian link is given by the "rubberband" Brunnian Links, where each component is looped around the next as aba −1 b −1, with the last looping around the first, forming a circle.