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For a unit circle with parametric equations x = cost (1) y = sint, (2) the negative pedal curve with respect to the pedal point (r,0) is x_n = (r-cost)/(rcost-1) (3) y_n = ...

The radical circle of the Lucas circles is the circumcircle of the Lucas tangents triangle. Its center has trilinear center function alpha_(1151)=2cosA+sinA (1) corresponding ...

The Moses-Longuet-Higgins circle is the radical circle of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c-a, c+a-b, and ...

The tangential mid-arc circle is the circumcircle of the tangential mid-arc triangle. Its center and radius appear to be very complicated functions. Its center is not in ...

If P is any point on a line TT^' whose orthopole is S, then the circle power of S with respect to the pedal circle of P is a constant (Gallatly 1913, p. 51).

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

Let A, B, and C be three circles in the plane, and let X be any circle touching B and C. Then build up a chain of circles such that Y:CAX, Z:ABY, X^':BCZ, Y^':CAX^', ...

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a ...

If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...