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In its simplest form, the principle of permanence states that, given any analytic function f(z) defined on an open (and connected) set U of the complex numbers C, and a ...

The case of the Weierstrass elliptic function with invariants g_2=-1 and g_3=0. The half-periods for this case are L(1+i)/4 and L(-1+i)/4, where L is the lemniscate constant ...

A quintic surface is an algebraic surface of degree 5. Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not ...

The regular nonagon is the regular polygon with nine sides and Schläfli symbol {9}. The regular nonagon cannot be constructed using the classical Greek rules of geometric ...

A rook polynomial is a polynomial R_(m,n)(x)=sum_(k=0)^(min(m,n))r_kx^k (1) whose number of ways k nonattacking rooks can be arranged on an m×n chessboard. The rook ...

Rosser's rule states that every Gram block contains the expected number of roots, which appears to be true for computable Gram blocks. Rosser et al. (1969) expressed a belief ...

In the arbelos, consider the semicircles K_1 and K_2 with centers A and C passing through B. The Apollonius circle K_3 of K_1, K_2 and the large semicircle of the arbelos is ...

A function f in C^infty(R^n) is called a Schwartz function if it goes to zero as |x|->infty faster than any inverse power of x, as do all its derivatives. That is, a function ...

Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a ...

The triangle DeltaN_1N_2N_3 formed by joining a set of three Neuberg centers (i.e., centers of the Neuberg circles) obtained from the edges of a given triangle DeltaA_1A_2A_3 ...