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The height of a tree g is defined as the vertex height of its root vertex, where the vertex height of a vertex v in a tree g is the number of edges on the longest downward ...

The ratio X_1/X_2 of uniform variates X_1 and X_2 on the interval [0,1] can be found directly as P_(X_1/X_2)(u) = int_0^1int_0^1delta((x_1)/(x_2)-u)dx_1dx_2 (1) = ...

Given a succession of nonsingular points which are on a nonhyperelliptic curve of curve genus p, but are not a group of the canonical series, the number of groups of the ...

The constant polynomial P(x)=0 whose coefficients are all equal to 0. The corresponding polynomial function is the constant function with value 0, also called the zero map. ...

Let phi_0 be the latitude for the origin of the Cartesian coordinates and lambda_0 its longitude, and let phi_1 and phi_2 be the standard parallels. Then for a unit sphere, ...

Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...

The 60 Pascal lines of a hexagon inscribed in a conic intersect three at a time through 20 Steiner points, and also three at a time in 60 Kirkman points. Each Steiner point ...

A circumconic is a conic section that passes through the vertices of a triangle (Kimberling 1998, p. 235). Every circumconic has a trilinear equation of the form ...

A conic projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cone with apex A which tangent to the ...

The conic sections are the nondegenerate curves generated by the intersections of a plane with one or two nappes of a cone. For a plane perpendicular to the axis of the cone, ...