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A periodic minimal surface constructed by Schwarz using the following two principles: 1. If part of the boundary of a minimal surface is a straight line, then the reflection ...

The space groups in two dimensions are called wallpaper groups. In three dimensions, the space groups are the symmetry groups possible in a crystal lattice with the ...

Smale (1958) proved that it is mathematically possible to turn a sphere inside-out without introducing a sharp crease at any point. This means there is a regular homotopy ...

When referring to a planar object, "free" means that the object is regarded as capable of being picked up out of the plane and flipped over. As a result, mirror images are ...

The square knot, also called the reef knot, is a composite knot of six crossings consisting of a knot sum of a trefoil knot and its mirror image (Rolfsen 1976, p. 220). The ...

A 1-variable unoriented knot polynomial Q(x). It satisfies Q_(unknot)=1 (1) and the skein relationship Q_(L_+)+Q_(L_-)=x(Q_(L_0)+Q_(L_infty)). (2) It also satisfies ...

An n-bridge knot is a knot with bridge number n. The set of 2-bridge knots is identical to the set of rational knots. If L is a 2-bridge knot, then the BLM/Ho polynomial Q ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

Rule 182 is one of the elementary cellular automaton rules introduced by Stephen Wolfram in 1983 (Wolfram 1983, 2002). It specifies the next color in a cell, depending on its ...

A pair of identical plane regions (mirror symmetric about two perpendicular lines through the center) which can be stitched together to form a baseball (or tennis ball). A ...