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The quantity ps-rq obtained by letting x = pX+qY (1) y = rX+sY (2) in ax^2+2bxy+cy^2 (3) so that A = ap^2+2bpr+cr^2 (4) B = apq+b(ps+qr)+crs (5) C = aq^2+2bqs+cs^2 (6) and ...

The point at which the three lines connecting the vertices of two perspective triangles concur, sometimes also called the perspective center, homology center, or pole. In the ...

An alternating permutation is an arrangement of the elements c_1, ..., c_n such that no element c_i has a magnitude between c_(i-1) and c_(i+1) is called an alternating (or ...

A sum is the result of an addition. For example, adding 1, 2, 3, and 4 gives the sum 10, written 1+2+3+4=10. (1) The numbers being summed are called addends, or sometimes ...

The logarithmic spiral is a spiral whose polar equation is given by r=ae^(btheta), (1) where r is the distance from the origin, theta is the angle from the x-axis, and a and ...

Let T be a central triangle and let U(T) be its unary cofactor triangle. Then T and U(T) are perspective, and their perspector is called the eigencenter of T. Let the A-, B-, ...

The radical line, also called the radical axis, is the locus of points of equal circle power with respect to two nonconcentric circles. By the chordal theorem, it is ...

The Euler polynomial E_n(x) is given by the Appell sequence with g(t)=1/2(e^t+1), (1) giving the generating function (2e^(xt))/(e^t+1)=sum_(n=0)^inftyE_n(x)(t^n)/(n!). (2) ...

The point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian ...

The intersection H of the three altitudes AH_A, BH_B, and CH_C of a triangle is called the orthocenter. The name was invented by Besant and Ferrers in 1865 while walking on a ...