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The direct product of the rings R_gamma, for gamma some index set I, is the set product_(gamma in I)R_gamma={f:I-> union _(gamma in I)R_gamma|f(gamma) in R_gamma all gamma in ...

dN^^+kappa_idr=0, where N^^ is the unit normal vector and kappa_i is one of the two principal curvatures.

The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count 2(m; 2)(n; 2), where (n; k) is a binomial ...

sum_(k=0)^dr_k^B(d-k)!x^k=sum_(k=0)^d(-1)^kr_k^(B^_)(d-k)!x^k(x+1)^(d-k).

If any of the roots of a polynomial are increased, then all of the critical points increase.

In the illusion illustrated above, when the concentric square borders with rounded edges are rotated slowly, the entire pattern appears to pulsate radially.

If the matrices A, X, B, and C satisfy AX-XB=C, then [I X; 0 I][A C; 0 B][I -X; 0 I]=[A 0; 0 B], where I is the identity matrix.

The curve b(u) in the ruled surface parameterization x(u,v)=b(u)+vd(u) is called the directrix (or base curve).

A specification of elements in a list as a list of pairs giving the element and number of times it occurs in a run. For example, given the list ...

A Greek cross rotated by 45 degrees, also called the crux decussata, illustrated schematically above in polyomino form. The multiplication sign × is based on Saint Andrew's ...