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A magic square that remains magic when its border is removed. A nested magic square remains magic after the border is successively removed one ring at a time. An example of a ...

The nonconservation of adiabatic invariants which arises in systems with three or more degrees of freedom.

The partial differential equation u_t+u_x+uu_x-u_(xxt)=0 (Benjamin et al. 1972; Arvin and Goldstein 1985; Zwillinger 1997, p. 130). A generalized version is given by u_t-del ...

An invariant set S subset R^n is said to be a C^r (r>=1) invariant manifold if S has the structure of a C^r differentiable manifold (Wiggins 1990, p. 14). When stable and ...

An n×n Latin square is a Latin rectangle with k=n. Specifically, a Latin square consists of n sets of the numbers 1 to n arranged in such a way that no orthogonal (row or ...

Every Möbius strip dissection of unequal squares can be glued along its edge to produce a dissection of the Klein bottle. There are no other ways to tile a Klein bottle with ...

If replacing each number by its square in a magic square produces another magic square, the square is said to be a bimagic square. Bimagic squares are also called doubly ...

A the (first, or internal) Kenmotu point, also called the congruent squares point, is the triangle center constructed by inscribing three equal squares such that each square ...

Consider three squares erected externally on the sides of a triangle DeltaABC. Call the centers of these squares O_A, O_B, and O_C, respectively. Then the lines AO_A, BO_B, ...

A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which ...