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An elliptic curve is the set of solutions to an equation of the form y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6. (1) By changing variables, y->2y+a_1x+a_3, assuming the field ...

A fallacy is an incorrect result arrived at by apparently correct, though actually specious reasoning. The great Greek geometer Euclid wrote an entire book on geometric ...

A finite sequence of real numbers {a_k}_(k=1)^n is said to be logarithmically concave (or log-concave) if a_i^2>=a_(i-1)a_(i+1) holds for every a_i with 1<=i<=n-1. A ...

A principal ideal domain is an integral domain in which every proper ideal can be generated by a single element. The term "principal ideal domain" is often abbreviated P.I.D. ...

The binary quadratic form F=<a,b,c> is said to be reduced if the following conditions hold. Let D=b^2-4ac be the discriminant, then 1. If D is negative, F is reduced if ...

A mathematical object defined for a set and a binary operator in which the multiplication operation is associative. No other restrictions are placed on a semigroup; thus a ...

The fundamental group of an arcwise-connected set X is the group formed by the sets of equivalence classes of the set of all loops, i.e., paths with initial and final points ...

The general bivariate quadratic curve can be written ax^2+2bxy+cy^2+2dx+2fy+g=0. (1) Define the following quantities: Delta = |a b d; b c f; d f g| (2) J = |a b; b c| (3) I = ...

The Berlekamp-van Lint-Seidel graph is the Hamiltonian strongly regular graph on 243 vertices with parameters (243,22,1,2). It is also distance-regular with intersection ...

The Cassini ovals are a family of quartic curves, also called Cassini ellipses, described by a point such that the product of its distances from two fixed points a distance ...