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The circumcenter is the center O of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors. The trilinear coordinates of the ...

The isogonal conjugate X^(-1) of a point X in the plane of the triangle DeltaABC is constructed by reflecting the lines AX, BX, and CX about the angle bisectors at A, B, and ...

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three ...

An isosceles trapezoid (called an isosceles trapezium by the British; Bronshtein and Semendyayev 1997, p. 174) is trapezoid in which the base angles are equal and therefore ...

If x takes only nonnegative values, then P(x>=a)<=(<x>)/a. (1) To prove the theorem, write <x> = int_0^inftyxP(x)dx (2) = int_0^axP(x)dx+int_a^inftyxP(x)dx. (3) Since P(x) is ...

The Riemann-Lebesgue Lemma, sometimes also called Mercer's theorem, states that lim_(n->infty)int_a^bK(lambda,z)Csin(nz)dz=0 (1) for arbitrarily large C and "nice" ...

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

Construction of the angle pi/3=60 degrees produces a 30-60-90 triangle, which has angles theta=pi/3 and theta/2=pi/6. From the above diagram, write y=sintheta for the ...

Construction of the angle pi/6=30 degrees produces a 30-60-90 triangle, which has angles theta=pi/6 and 2theta=pi/3. From the above diagram, write y=sintheta for the vertical ...

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...