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Ellipses sharing common foci (left figure). The family of confocal ellipses covers the plane simply, in the sense that there is a unique ellipse passing through each point in ...

Hyperbolas sharing common foci (left figure). The family of confocal hyperbolas covers the plane simply, in the sense that there is a unique hyperbola passing through each ...

(x^2)/(a^2-lambda)+(y^2)/(b^2-lambda)=z-lambda (1) (x^2)/(a^2-mu)+(y^2)/(b^2-mu)=z-mu (2) (x^2)/(a^2-nu)+(y^2)/(b^2-nu)=z-nu, (3) where lambda in (-infty,b^2), mu in ...

A set of quadratic surfaces which share foci. Ellipsoids and one- and two-sheeted hyperboloids can be confocal. These three types of surfaces can be combined to form an ...

Conformal latitude is defined by chi = 2tan^(-1){tan(1/4pi+1/2phi)[(1-esinphi)/(1+esinphi)]^(e/2)}-1/2pi (1) = ...

A map projection which is a conformal mapping, i.e., one for which local (infinitesimal) angles on a sphere are mapped to the same angles in the projection. On maps of an ...

Given a triangle, draw a Cevian to one of the bases that divides it into two triangles having congruent incircles. The positions and sizes of these two circumcircles can then ...

The triangulation point Y of a reference triangle DeltaABC for which triangles DeltaBYC, DeltaCYA, and DeltaAYB have congruent incircles. It is a special case of an Elkies ...

In 1989, P. Yff proved there is a unique configuration of isoscelizers for a given triangle such that all three have the same length and are concurrent (C. Kimberling, pers. ...

The directrix of a conic section is the line which, together with the point known as the focus, serves to define a conic section as the locus of points whose distance from ...