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If three circles A, B, and C are taken in pairs, the external similarity points of the three pairs lie on a straight line. Similarly, the external similarity point of one ...
A box can be packed with a harmonic brick a×ab×abc iff the box has dimensions ap×abq×abcr for some natural numbers p, q, r (i.e., the box is a multiple of the brick).
The x-axis is the horizontal axis of a two-dimensional plot in Cartesian coordinates that is conventionally oriented to point to the right (left figure). In three dimensions, ...
The vertical axis of a two-dimensional plot in Cartesian coordinates. Physicists and astronomers sometimes call this axis the ordinate, although that term is more commonly ...
The cube-octahedron compound is a polyhedron compound composed of a cube and its dual polyhedron, the octahedron. It is implemented in the Wolfram Language as ...
A special case of Apollonius' problem requiring the determination of a circle touching three mutually tangent circles (also called the kissing circles problem). There are two ...
Bezdek and Kuperberg (1991) have constructed packings of identical ellipsoids of densities arbitrarily close to ((24sqrt(2)-6sqrt(3)-2pi)pi)/(72)=0.753355... (OEIS A093824), ...
The regular tessellation {6,3} consisting of regular hexagons (i.e., a hexagonal grid). In general, the term honeycomb is used to refer to a tessellation in n dimensions for ...
The hyperbolic octahedron is a hyperbolic version of the Euclidean octahedron, which is a special case of the astroidal ellipsoid with a=b=c=1. It is given by the parametric ...
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