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First stated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of ...

The tetragonal antiwedge is the topological class of hexahedron. It has 10 edges and 6 vertices and its faces consist of 4 triangles and 2 quadrilaterals. A tetragonal ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to ...

A composition of a function f degreesf with itself gives a nested function f(f(x)), f degreesf degreesf which gives f(f(f(x)), etc. Function nesting is implemented in the ...

Sylvester's line problem, known as the Sylvester-Gallai theorem in proved form, states that it is not possible to arrange a finite number of points so that a line through ...

Nonparametric estimation is a statistical method that allows the functional form of a fit to data to be obtained in the absence of any guidance or constraints from theory. As ...

Two square matrices A and B that are related by B=X^(-1)AX, (1) where X is a square nonsingular matrix are said to be similar. A transformation of the form X^(-1)AX is called ...

Curves with Cartesian equation ay^2=x(x^2-2bx+c) with a>0. The above equation represents the third class of Newton's classification of cubic curves, which Newton divided into ...

The perspective image of an infinite checkerboard. It can be constructed starting from any triangle DeltaOXY, where OX and OY form the near corner of the floor, and XY is the ...