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A 15-sided polygon, sometimes also called the pentakaidecagon. For a regular pentadecagon with side length 1, the inradius r, circumradius R, and area A are r = ...

A pentagon is a five-sided polygon. Several special types of pentagons are illustrated above. In particular, a pentagon with vertices equally spaced around a circle and with ...

The smallest radial distance of an ellipse as measured from a focus. Taking v=0 in the equation of an ellipse r=(a(1-e^2))/(1+ecosv) gives the periapsis distance r_-=a(1-e). ...

The line joining the three collinear points of intersection of the extensions of corresponding sides in perspective triangles, also called the perspectrix or homology axis.

The point at which the three lines connecting the polygon vertices of perspective triangles (from a point) concur, sometimes also called the homology center, pole, or, in ...

A curve composed exclusively of circular arcs.

A pivot point of a curve is a fixed point Q such that points P lying on the curve and their (isogonal, isotomic, etc.) conjugates are collinear with Q.

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. ...

Members of a coaxal system satisfy x^2+y^2+2lambdax+c=(x+lambda)^2+y^2+c-lambda^2=0 for values of lambda. Picking lambda^2=c then gives the two circles (x+/-sqrt(c))^2+y^2=0 ...

The positions of the geometric centroid of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) are x^_ = ...