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The group of an elliptic curve which has been transformed to the form y^2=x^3+ax+b is the set of K-rational points, including the single point at infinity. The group law ...

The approximation for pi given by pi approx sqrt((40)/3-2sqrt(3)) (1) = 1/3sqrt(120-18sqrt(3)) (2) = 3.141533.... (3) In the above figure, let OA=OF=1, and construct the ...

A polygonal diagonal is a line segment connecting two nonadjacent polygon vertices of a polygon. The number of ways a fixed convex n-gon can be divided into triangles by ...

For a diagonal metric tensor g_(ij)=g_(ii)delta_(ij), where delta_(ij) is the Kronecker delta, the scale factor for a parametrization x_1=f_1(q_1,q_2,...,q_n), ...

A function is a relation that uniquely associates members of one set with members of another set. More formally, a function from A to B is an object f such that every a in A ...

A tree (also called a bicentral tree) having two nodes that are graph centers. The numbers of bicentered trees on n=1, 2, ... nodes are 0, 1, 0, 1, 1, 3, 4, 11, 20, 51, 108 ...

The blow-up lemma essentially says that regular pairs in Szemerédi's regularity lemma behave like complete bipartite graphs from the point of view of embedding bounded degree ...

A set in which no element divides the sum of any nonempty subset of the other elements. For example, {2,3,5} is dividing, since 2|(3+5) (and 5|(2+3)), but {4,6,7} is ...

Four circles c_1, c_2, c_3, and c_4 are tangent to a fifth circle or a straight line iff T_(12)T_(34)+/-T_(13)T_(42)+/-T_(14)T_(23)=0. (1) where T_(ij) is the length of a ...

Connect-Four is a tic-tac-toe-like two-player game in which players alternately place pieces on a vertical board 7 columns across and 6 rows high. Each player uses pieces of ...