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A polyhedron is rigid if it cannot be continuously deformed into another configuration. A rigid polyhedron may have two or more stable forms which cannot be continuously ...

For every positive integer n, there exists a circle in the plane having exactly n lattice points on its circumference. The theorem is based on the number r(n) of integral ...

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 point T at which the lines through the polygon vertices of a triangle perpendicular to the corresponding sides of the first Brocard triangle, are concurrent. The Tarry ...

Consecutive number sequences are sequences constructed by concatenating numbers of a given type. Many of these sequences were considered by Smarandache and so are sometimes ...

A symmetry of a knot K is a homeomorphism of R^3 which maps K onto itself. More succinctly, a knot symmetry is a homeomorphism of the pair of spaces (R^3,K). Hoste et al. ...

The molecular topological index is a graph index defined by MTI=sum_(i=1)^nE_i, where E_i are the components of the vector E=(A+D)d, with A the adjacency matrix, D the graph ...

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. Its Schläfli symbol is {infty}. The apeirogon can produce a ...

Consider three mutually tangent circles, and draw their inner Soddy circle. Then draw the inner Soddy circles of this circle with each pair of the original three, and ...

Ball triangle picking is the selection of triples of points (corresponding to vertices of a general triangle) randomly placed inside a ball. n random triangles can be picked ...