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A tetramagic cube is a magic cube that remains magic when all its numbers are squared, cubed, and taken to the fourth power. Only two tetramagic cubes are known, and both ...

The Theodorus spiral, also known as the Einstein spiral, Pythagorean spiral, square root spiral, or--to contrast it with certain continuous analogs--the discrete spiral of ...

A square matrix is said to be totally positive if the determinant of any square submatrix, including the minors, is positive. For instance, any 2×2 matrix whose determinant ...

The tribox, also called the Penrose rectangle or Penrose square, is an impossible figure that is the generalization of the Penrose triangle from a triangle to a square. ...

Let L denote the n×n triangular lattice with wraparound. Call an orientation of L an assignment of a direction to each edge of L, and denote the number of orientations of L ...

A square matrix A is said to be unipotent if A-I, where I is an identity matrix is a nilpotent matrix (defined by the property that A^n is the zero matrix for some positive ...

A unit is an element in a ring that has a multiplicative inverse. If a is an algebraic integer which divides every algebraic integer in the field, a is called a unit in that ...

Two polygons are congruent by dissection iff they have the same area. In particular, any polygon is congruent by dissection to a square of the same area. Laczkovich (1988) ...

The complex numbers are the field C of numbers of the form x+iy, where x and y are real numbers and i is the imaginary unit equal to the square root of -1, sqrt(-1). When a ...

Let a chess piece make a tour on an n×n chessboard whose squares are numbered from 1 to n^2 along the path of the chess piece. Then the tour is called a magic tour if the ...