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If the cusp of the cardioid is taken as the inversion center, the cardioid inverts to a parabola.

For the cardioid given parametrically as x = a(1+cost)cost (1) y = a(1+cost)sint, (2) the involute is given by x_i = 2a+3acostheta(1-costheta) (3) y_i = ...

A map projection defined by x = sin^(-1)[cosphisin(lambda-lambda_0)] (1) y = tan^(-1)[(tanphi)/(cos(lambda-lambda_0))]. (2) The inverse formulas are phi = sin^(-1)(sinDcosx) ...

The envelope of the lines connecting corresponding points on the Jacobian curve and Steinerian curve. The Cayleyian curve of a net of curves of order n has the same curve ...

In mathematics, a cell is a finite regular polytope.

An ellipse or hyperbola.

Suppose P=p:q:r and U=u:v:w are points, neither lying on a sideline of DeltaABC. Then the cevapoint of P and U is the point (pv+qu)(pw+ru):(qw+rv)(qu+pv) :(ru+pw)(rv+qw).

A sequence of circles which closes (such as a Steiner chain or the circles inscribed in the arbelos) is called a chain.

The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known ...

In Homogeneous coordinates (x_1,x_2,x_3), the equation of a circle C is a(x_1^2+x_2^2)+2fx_2x_3+2gx_1x_3+cx_3^2=0. The discriminant of this circle is defined as Delta=|a 0 g; ...