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A cube 30-compound can be constructed from the vertices of the first dodecahedron 6-compound. It will be implemented in a future version of the Wolfram Language as ...

An illusion due to Franz Joseph Delboeuf, a Belgian philosopher and expert on hypnosis. If the same circle is placed inside two different concentric circles, its size will ...

Differential calculus is that portion of "the" calculus dealing with derivatives. Among his many other talents, Major General Stanley in Gilbert and Sullivan's operetta the ...

The computation of a derivative.

A notation invented by Dirac which is very useful in quantum mechanics. The notation defines the "ket" vector, denoted |psi>, and its conjugate transpose, called the "bra" ...

The Dirichlet kernel D_n^M is obtained by integrating the number theoretic character e^(i<xi,x>) over the ball |xi|<=M, D_n^M=-1/(2pir)d/(dr)D_(n-2)^M.

Handles and cross-handles are equivalent in the presence of a cross-cap.

The edge set of a graph is simply a set of all edges of the graph. The cardinality of the edge set for a given graph g is known as the edge count of g. The edge set for a ...

For any integers a_i with 1<=a_1<a_2<...<a_k<=n, the proportion of permutations in the symmetric group S_n whose cyclic decompositions contain no cycles of lengths a_1, a_2, ...

An endomorphism is called ergodic if it is true that T^(-1)A=A implies m(A)=0 or 1, where T^(-1)A={x in X:T(x) in A}. Examples of ergodic endomorphisms include the map X->2x ...