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"Escher's solid" is the solid illustrated on the right pedestal in M. C. Escher's Waterfall woodcut (Bool et al. 1982, p. 323). It is obtained by augmenting a rhombic ...

The norm of a mathematical object is a quantity that in some (possibly abstract) sense describes the length, size, or extent of the object. Norms exist for complex numbers ...

There are several attractive polyhedron compounds consisting of three cubes. The first (left figures) arises by joining three cubes such that each shares two C_2 axes (Holden ...

Given a function f(x_1,...,x_n) defined on a domain U, the graph of f is defined as the set of points (which often form a curve or surface) showing the values taken by f over ...

The tangent plane to a surface at a point p is the tangent space at p (after translating to the origin). The elements of the tangent space are called tangent vectors, and ...

A parameterization of a minimal surface in terms of two functions f(z) and g(z) as [x(r,phi); y(r,phi); z(r,phi)]=Rint[f(1-g^2); if(1+g^2); 2fg]dz, where z=re^(iphi) and R[z] ...

On the Clebsch diagonal cubic, all 27 of the complex lines present on a general smooth cubic surface are real. In addition, there are 10 points on the surface where three of ...

An area-minimizing surface (rectifiable current) bounded by a smooth curve in R^3 is a smooth submanifold with boundary.

The word "base" in mathematics is used to refer to a particular mathematical object that is used as a building block. The most common uses are the related concepts of the ...

The lemniscate, also called the lemniscate of Bernoulli, is a polar curve defined as the locus of points such that the the product of distances from two fixed points (-a,0) ...