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The centroid is center of mass of a two-dimensional planar lamina or a three-dimensional solid. The mass of a lamina with surface density function sigma(x,y) is ...

An affine variety V is an algebraic variety contained in affine space. For example, {(x,y,z):x^2+y^2-z^2=0} (1) is the cone, and {(x,y,z):x^2+y^2-z^2=0,ax+by+cz=0} (2) is a ...

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 ...

A curve of order n is generally determined by n(n+3)/2 points. So a conic section is determined by five points and a cubic curve should require nine. But the Maclaurin-Bézout ...

If S_1, S_2, and S_3 are three conics having the property that there is a point X, not on any of the conics, lying on a common chord of each pair of the three conics (with ...

An isolated singularity is a singularity for which there exists a (small) real number epsilon such that there are no other singularities within a neighborhood of radius ...

Let three similar isosceles triangles DeltaA^'BC, DeltaAB^'C, and DeltaABC^' be constructed on the sides of a triangle DeltaABC. Then DeltaABC and DeltaA^'B^'C^' are ...