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If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the ...

The definite integral int_a^bx^ndx={(b^(n+1)-a^(n+1))/(n+1) for n!=1; ln(b/a) for n=-1, (1) where a, b, and x are real numbers and lnx is the natural logarithm.

The (connected) caveman graph is a graph arising in social network theory formed by modifying a set of isolated k-cliques (or "caves") by removing one edge from each clique ...

Let X_1,X_2 subset P^2 be cubic plane curves meeting in nine points p_1, ..., p_9. If X subset P^2 is any cubic containing p_1, ..., p_8, then X contains p_9 as well. It is ...

Given A = |a_(11)-x a_(12) ... a_(1m); a_(21) a_(22)-x ... a_(2m); | | ... |; a_(m1) a_(m2) ... a_(mm)-x| (1) = x^m+c_(m-1)x^(m-1)+...+c_0, (2) then ...

The metric of Felix Klein's model for hyperbolic geometry, g_(11) = (a^2(1-x_2^2))/((1-x_1^2-x_2^2)^2) (1) g_(12) = (a^2x_1x_2)/((1-x_1^2-x_2^2)^2) (2) g_(22) = ...

The parameters alpha, beta, gamma, and delta which, like the three Euler angles, provide a way to uniquely characterize the orientation of a solid body. These parameters ...

The Cayley-Menger determinant is a determinant that gives the volume of a simplex in j dimensions. If S is a j-simplex in R^n with vertices v_1,...,v_(j+1) and B=(beta_(ik)) ...

The Cayley-Purser algorithm is a public-key cryptography algorithm that relies on the fact that matrix multiplication is not commutative. It was devised by Sarah Flannery ...

The only nonassociative division algebra with real scalars. There is an 8-square identity corresponding to this algebra. The elements of a Cayley algebra are called Cayley ...