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Monster-barring is a term coined by Lakatos (1976) to refer to the refining of a hypothesis to rule out nasty counterexamples (Bailey et al. 2007, p. 11).

The illusion illustrated above in which the bounding rectangle and inner square both appear distorted.

The Pell constant is the infinite product P = 1-product_(k=0)^(infty)(1-1/(2^(2k+1))) (1) = 1-(1/2;1/4)_infty (2) = 0.58057755820489... (3) (OEIS A141848), where (a,q)_infty ...

An ideal I of a ring R is called principal if there is an element a of R such that I=aR={ar:r in R}. In other words, the ideal is generated by the element a. For example, the ...

For a quadrilateral which is not cyclic, Ptolemy's theorem becomes an inequality: AB×CD+BC×DA>AC×BD. The Ptolemy inequality is still valid when ABCD is a triangular pyramid ...

The analog of trilinear coordinates for tetrahedra.

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

Suppose for every point x in a manifold M, an inner product <·,·>_x is defined on a tangent space T_xM of M at x. Then the collection of all these inner products is called ...

An operator T which commutes with all shift operators E^a, so TE^a=E^aT for all real a in a field. Any two shift-invariant operators commute.

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.