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Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of ...

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 ...

An incircle is an inscribed circle of a polygon, i.e., a circle that is tangent to each of the polygon's sides. The center I of the incircle is called the incenter, and the ...

The truncated octahedron is the 14-faced Archimedean solid with faces 8{6}+6{4}. It is also the uniform polyhedron with Maeder index 8 (Maeder 1997), Wenninger index 7 ...

A Turing machine is a theoretical computing machine invented by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine consists of a ...

Abstract Algebra

The residue classes of a function f(x) mod n are all possible values of the residue f(x) (mod n). For example, the residue classes of x^2 (mod 6) are {0,1,3,4}, since 0^2=0 ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

The 11-cell is a regular 4-dimensional structure that cannot be represented in 3-dimensional space in any reasonable way and is highly self-intersecting even in 4-dimensional ...

The insphere of a solid is a sphere that is tangent to all faces of the solid. An insphere does not always exist, but when it does, its radius r is called the inradius and ...