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A triangle DeltaA^'B^'C^' is said to be circumscribed in a triangle DeltaABC if A lies on B^'C^', B lies on C^'A^', and C lies on A^'B^' (Kimberling 1998, p. 185). Examples ...

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 ...

Cis(x) is another name for the complex exponential, Cis(x)=e^(ix)=cosx+isinx. (1) It has derivative d/(dz)Cis(z)=ie^(iz) (2) and indefinite integral intCis(z)dz=-ie^(iz). (3)

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 ...

A cubic curve invented by Diocles in about 180 BC in connection with his attempt to duplicate the cube by geometrical methods. The name "cissoid" first appears in the work of ...

For the parametric representation x = (2t^2)/(1+t^2) (1) y = (2t^3)/(1+t^2), (2) the catacaustic of this curve from the radiant point (8a,0) is given by x = ...

If the cusp of the cissoid of Diocles is taken as the inversion center, then the cissoid inverts to a parabola.

The pedal curve of the cissoid, when the pedal point is on the axis beyond the asymptote at a distance from the cusp which is four times that of the asymptote is a cardioid.

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," ...