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The pedal curve of a logarithmic spiral with parametric equation f = e^(at)cost (1) g = e^(at)sint (2) for a pedal point at the pole is an identical logarithmic spiral x = ...

The MacBeath circle, a term coined here for the first time, is the circumcircle of the MacBeath triangle. It has a fairly complicated radius, center function, and circle ...

The involute of the nephroid given by x = 1/2[3cost-cos(3t)] (1) y = 1/2[3sint-sin(3t)] (2) beginning at the point where the nephroid cuts the y-axis is given by x = 4cos^3t ...

A plane coordinate system whose axes are not perpendicular. The x-coordinate of a point P is the abscissa of its projection onto the x-axis in the direction of the y-axis, ...

The orthocubic (or ortho cubic) Z(X_4) is a self-isogonal cubic with pivot point at the orthocenter H, so it has parameter x=cosBcosC and trilinear equation (Cundy and Parry ...

If a circular pizza is divided into 8, 12, 16, ... slices by making cuts at equal angles from an arbitrary point, then the sums of the areas of alternate slices are equal. ...

Consider the plane figure obtained by drawing each diagonal in a regular polygon. If each point of intersection is associated with a node and diagonals are split ar each ...

Let j, r, and s be distinct integers (mod n), and let W_i be the point of intersection of the side or diagonal V_iV_(i+j) of the n-gon P=[V_1,...,V_n] with the transversal ...

A symplectic form on a smooth manifold M is a smooth closed 2-form omega on M which is nondegenerate such that at every point m, the alternating bilinear form omega_m on the ...

The x-axis is the horizontal axis of a two-dimensional plot in Cartesian coordinates that is conventionally oriented to point to the right (left figure). In three dimensions, ...