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The partial differential equation u_(tt)-u_(xx)-u+u^3=0.

Virtually nothing is known about dissection of a projective plane using unequal squares.

The dual polyhedron of the rhombicosahedron U_(56) and Wenninger dual W_(96).

A correspondence between a permutation and a pair of Young tableaux.

An operator E such that E^ap(x)=p(x+a).

Two figures are homothetic if they are related by a dilation (a dilation is also known as a homothecy). This means that the connectors of corresponding points are concurrent ...

A simple pole of an analytic function f is a pole of order one. That is, (z-z_0)f(z) is an analytic function at the pole z=z_0. Alternatively, its principal part is c/(z-z_0) ...

Consecutive Smith numbers. The first few Smith brothers are (728, 729), (2964, 2965), (3864, 3865), (4959, 4960), ... (OEIS A050219 and A050220).

An ordinary knot in three dimensions suspended in four dimensions to create a knotted 2-sphere. Suspended knots are not smooth at the poles.

A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...