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The hexagonal packing of circles on a 2-dimensional Euclidean plane. These problems are mathematically distinct from the ideas in the circle packing theorem.The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere.
The hexagonal gaps can be filled by one circle and the dodecagonal gaps can be filled with seven circles, creating 3-uniform packings. The truncated trihexagonal tiling with both types of gaps can be filled as a 4-uniform packing. The snub hexagonal tiling has two mirror-image forms.
Square packing in a circle is a related problem of packing n unit squares into a circle with radius as small as possible. For this problem, good solutions are known for n up to 35. Here are the minimum known solutions for up to n =12: [ 11 ] (Only the cases n=1 and n=2 are known to be optimal)
List of mathematical topics; List of statistical topics; List of mathematical functions; List of mathematical theorems; List of mathematical proofs; List of matrices
A circle packing for a five-vertex planar graph. The circle packing theorem (also known as the Koebe–Andreev–Thurston theorem) describes the possible tangency relations between circles in the plane whose interiors are disjoint. A circle packing is a connected collection of circles (in general, on any Riemann surface) whose interiors are ...
The initialism Q.E.D. or QED (Latin: quod erat demonstrandum, "as was to be shown") is often used for the same purpose, either in its upper-case form or in lower case. Bourbaki dangerous bend symbol : Sometimes used in the margin to forewarn readers against serious errors, where they risk falling, or to mark a passage that is tricky on a first ...
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