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The van der Grinten projection is a map projection given by the transformation x = (1) y = sgn(phi)(pi|PQ-Asqrt((A^2+1)(P^2+A^2)-Q^2)|)/(P^2+A^2), (2) where A = ...

The differential equation describing exponential growth is (dN)/(dt)=rN. (1) This can be integrated directly int_(N_0)^N(dN)/N=int_0^trdt (2) to give ln(N/(N_0))=rt, (3) ...

The Jacobian conjecture in the plane, first stated by Keller (1939), states that given a ring map F of C[x,y] (the polynomial ring in two variables over the complex numbers ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

An abnormal number is a hypothetical number which can be factored into primes in more than one way. Hardy and Wright (1979) prove the fundamental theorem of arithmetic by ...

An accumulation point is a point which is the limit of a sequence, also called a limit point. For some maps, periodic orbits give way to chaotic ones beyond a point known as ...

A ruled surface M is said to be a binormal developable of a curve y if M can be parameterized by x(u,v)=y(u)+vB^^(u), where B is the binormal vector.

The boustrophedon ("ox-plowing") transform b of a sequence a is given by b_n = sum_(k=0)^(n)(n; k)a_kE_(n-k) (1) a_n = sum_(k=0)^(n)(-1)^(n-k)(n; k)b_kE_(n-k) (2) for n>=0, ...

Two square matrices A and B are called congruent if there exists a nonsingular matrix P such that B=P^(T)AP, where P^(T) is the transpose.

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.