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For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...

The inner Vecten circle is the circumcircle of the inner Vecten triangle. It has center at Kimberling center X_(642), which is the complement of the inner Vecten point ...

The MacBeath triangle DeltaX_AX_BX_C (a term coined here for the first time), is the triangle whose vertices are the contact points of the MacBeath inconic with the reference ...

A similar construction can be done by initially erecting a square internally on the side BC. This leads to the A^--inscribed square. The triangle DeltaX^-Y^-Z^- of centers of ...

The Yff contact circle is the circumcircle of the Yff contact triangle. Its center has triangle center function alpha=((b-c)(3a^3+b^3+c^3-2a^2b-2a^2c-abc))/a, (1) which does ...

Take any triangle with polygon vertices A, B, and C. Pick a point A_1 on the side opposite A, and draw a line parallel to BC. Upon reaching the side AC at B_1, draw the line ...

A fixed point for which the stability matrix has one zero eigenvector with negative eigenvalue lambda<0.

A fixed point for which the stability matrix has one zero eigenvector with positive eigenvalue lambda>0.

In general, the pedal curve of the cardioid is a slightly complicated function. The pedal curve of the cardioid with respect to the center of its conchoidal circle is the ...

The elastica formed by bent rods and considered in physics can be generalized to curves in a Riemannian manifold which are a critical point for ...