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The area of the dodecagon (n=12) inscribed in a unit circle with R=1 is A=1/2nR^2sin((2pi)/n)=3.

A lattice which is built up of layers of n-dimensional lattices in (n+1)-dimensional space. The vectors specifying how layers are stacked are called glue vectors. The order ...

A submodule L of a module M such that for any other nonzero submodule K of M, the intersection L intersection K is not the zero module. L is also called an essential ...

A law in (2-valued) logic which states there is no third alternative to truth or falsehood. In other words, for any statement A, either A or not-A must be true and the other ...

The inverse curve of a lemniscate in a circle centered at the origin and touching the lemniscate where it crosses the x-axis produces a rectangular hyperbola (Wells 1991).

The infinitesimal algebraic object associated with a Lie groupoid. A Lie algebroid over a manifold B is a vector bundle A over B with a Lie algebra structure [,] (Lie ...

Limacon Evolute The catacaustic of a circle for a radiant point is the limaçon evolute. It has parametric equations x = (a[4a^2+4b^2+9abcost-abcos(3t)])/(4(2a^2+b^2+3abcost)) ...

The line bisecting a given line segment P_1P_2 can be constructed geometrically, as illustrated above.

product_(i)dp_idq_i, where p_i and q_i are momenta and positions of particles.

In space, the only conformal mappings are inversions, similarity transformations, and congruence transformations. Or, restated, every angle-preserving transformation is a ...