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The dimension of an object is a topological measure of the size of its covering properties. Roughly speaking, it is the number of coordinates needed to specify a point on the ...

The fundamental group of an arcwise-connected set X is the group formed by the sets of equivalence classes of the set of all loops, i.e., paths with initial and final points ...

The n-hypersphere (often simply called the n-sphere) is a generalization of the circle (called by geometers the 2-sphere) and usual sphere (called by geometers the 3-sphere) ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

The regular pentagon is the regular polygon with five sides, as illustrated above. A number of distance relationships between vertices of the regular pentagon can be derived ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular ...

A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with n graph vertices is denoted K_n and has (n; 2)=n(n-1)/2 (the ...

A Hamiltonian cycle, also called a Hamiltonian circuit, Hamilton cycle, or Hamilton circuit, is a graph cycle (i.e., closed loop) through a graph that visits each node ...

"The" octahedral graph is the 6-node 12-edge Platonic graph having the connectivity of the octahedron. It is isomorphic to the circulant graph Ci_6(1,2), the cocktail party ...