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The perpendicular distance h from an arc's midpoint to the chord across it, equal to the radius R minus the apothem r, h=R-r. (1) For a regular polygon of side length a, h = ...

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 ...

Lachlan's term for a set of four points, no three of which are collinear.

The three-chord lemma states that in the figure above, l_1+l_2=2lcostheta.

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three ...

The Trott curve is a simple example of a quartic curve having 28 real bitangents-the maximum possible for a quartic-given by the equation ...

The point about which an angle is measured is called the angle's vertex, and the angle theta associated with a given vertex is called the vertex angle. In a polygon, the ...

A (-1,0,1)-matrix is a matrix whose elements consist only of the numbers -1, 0, or 1. The number of distinct (-1,0,1)-n×n matrices (counting row and column permutations, the ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

The points of tangency t_1 and t_2 for the four lines tangent to two circles with centers x_1 and x_2 and radii r_1 and r_2 are given by solving the simultaneous equations ...