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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 ...

A subset G subset R of the real numbers is said to be a G_delta set provided G is the countable intersection of open sets. The name G_delta comes from German: The G stands ...

The initial side of an angle theta drawn in angle standard position is the side lying on the positive x-axis. In general, viewing an angle as the amount of rotation about the ...

According to G. Pólya, the method of finding geometric objects by intersection. 1. For example, the centers of all circles tangent to a straight line s at a given point P lie ...

If we expand the determinant of a matrix A using determinant expansion by minors, first in terms of the minors of order r formed from any r rows, with their complementaries, ...

A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

Let X be a set and S a collection of subsets of X. A subset A subset X is shattered by S if each subset B subset A of A can be expressed as the intersection of A with a ...

The equation of the curve of intersection of a torus with a plane perpendicular to both the midplane of the torus and to the plane x=0. (The general intersection of a torus ...

In the above figure, let DeltaABC be a right triangle, arcs AP and AQ be segments of circles centered at C and B respectively, and define a = BC (1) b = CA=CP (2) c = BA=BQ. ...

In the usual diagram of inclusion homomorphisms, if the upper two maps are injective, then so are the other two. More formally, consider a space X which is expressible as the ...