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A universal differential equation (UDE) is a nontrivial differential-algebraic equation with the property that its solutions approximate to arbitrary accuracy any continuous ...

The vertex figure at a vertex V of a polygon is the line segment joining the midpoints of the two adjacent sides meeting at V. For a regular n-gon with side length a, the ...

A surface which can be interpreted as a self-intersecting rectangle in three dimensions. The Whitney umbrella is the only stable singularity of mappings from R^2 to R^3. It ...

An inconic with parameters x:y:z=a(b-c):b(c-a):c(a-b), (1) giving equation (2) (Kimberling 1998, pp. 238-239). Its focus is Kimberling center X_(101) and its conic section ...

A zonotope is a set of points in d-dimensional space constructed from vectors v_i by taking the sum of a_iv_i, where each a_i is a scalar between 0 and 1. Different choices ...

An algebraic surface of order 3. Schläfli and Cayley classified the singular cubic surfaces. On the general cubic, there exists a curious geometrical structure called double ...

Kobon Fujimura asked for the largest number N(n) of nonoverlapping triangles that can be constructed using n lines (Gardner 1983, p. 170). A Kobon triangle is therefore ...

Two lines or plane congruent geometric figures which lie on top of each other are said to be coincident.

The slicing of a three-dimensional object by a plane (or more general slice).

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 ...