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A class of illusion in which an object which is physically unrealizable is apparently depicted. More than 100 papers have been written about impossible figures (Kulpa 1987), ...

If two points A and A^' are inverse with respect to a circle (the inversion circle), then the straight line through A^' which is perpendicular to the line of the points AA^' ...

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 ...

There are a number of functions in mathematics commonly denoted with a Greek letter lambda. Examples of one-variable functions denoted lambda(n) with a lower case lambda ...

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 ...

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2), (3) and an ...

In the case of a general surface, the distance between two points measured along the surface is known as a geodesic. For example, the shortest distance between two points on ...

d_n=p_(n+1)-p_n. (1) The first few values are 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, ... (OEIS A001223). Rankin has shown that d_n>(clnnlnlnnlnlnlnlnn)/((lnlnlnn)^2) ...

The radical lines of three circles are concurrent in a point known as the radical center (also called the power center). This theorem was originally demonstrated by Monge ...

The rational distance problem asks to find a geometric configuration satisfying given properties such that all distances along specific edges are rational numbers. (This is ...