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Let a convex cyclic polygon be triangulated in any manner, and draw the incircle to each triangle so constructed. Then the sum of the inradii is a constant independent of the ...

If J is a simple closed curve in R^2, then the Jordan curve theorem, also called the Jordan-Brouwer theorem (Spanier 1966) states that R^2-J has two components (an "inside" ...

A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely ...

There are at least 15 classes of convex pentagonal tilings, as illustrated above. The first five were discovered during investigations of German mathematician Karl Reinhardt ...

If a Steiner chain is formed from one starting circle, then a Steiner chain is formed from any other starting circle. In other words, given two circles with one interior to ...

The bicorn, sometimes also called the "cocked hat curve" (Cundy and Rollett 1989, p. 72), is the name of a collection of quartic curves studied by Sylvester in 1864 and ...

Inscribe a triangle in a circle such that the sides of the triangle pass through three given points A, B, and C.

The dihedral angle is the angle theta between two planes. The dihedral angle between the planes a_1x+b_1y+c_1z+d_1 = 0 (1) a_2x+b_2y+c_2z+d_2 = 0 (2) which have normal ...

The elliptic exponential function eexp_(a,b)(u) gives the value of x in the elliptic logarithm eln_(a,b)(x)=1/2int_infty^x(dt)/(sqrt(t^3+at^2+bt)) for a and b real such that ...

The envelope of a one-parameter family of curves given implicitly by U(x,y,c)=0, (1) or in parametric form by (f(t,c),g(t,c)), is a curve that touches every member of the ...