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The circumcircle mid-arc triangle is the triangle whose vertices are given by the circumcircle mid-arc points of a given reference triangle. Its trilinear vertex matrix is ...

A circumellipse is a circumconic of a triangle that is an ellipse. There is an amazing formula for the area of a circumellipse. Let d_A be the length of the chord of the ...

The circumnormal triangle is an equilateral triangle with vertices on the circumcircle of a reference triangle DeltaABC obtained by rotating the circumtangential triangle by ...

The circumsphere of given set of points, commonly the vertices of a solid, is a sphere that passes through all the points. A circumsphere does not always exist, but when it ...

The circumtangential triangle is an equilateral triangle formed by the three points X on the circumcircle of a reference triangle DeltaABC at which the line XX^(-1), where ...

Given two curves C_1 and C_2 and a fixed point O, let a line from O cut C_1 at Q and C_2 at R. Then the locus of a point P such that OP=QR is the cissoid. The word cissoid ...

Clairaut's difference equation is a special case of Lagrange's equation (Sokolnikoff and Redheffer 1958) defined by u_k=kDeltau_k+F(Deltau_k), (1) or in "x notation," ...

y=x(dy)/(dx)+f((dy)/(dx)) (1) or y=px+f(p), (2) where f is a function of one variable and p=dy/dx. The general solution is y=cx+f(c). (3) The singular solution envelopes are ...

Clark's triangle is a number triangle created by setting the vertex equal to 0, filling one diagonal with 1s, the other diagonal with multiples of an integer f, and filling ...

Let O be an order of an imaginary quadratic field. The class equation of O is the equation H_O=0, where H_O is the extension field minimal polynomial of j(O) over Q, with ...