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A torus with a hole that can eat another torus. The transformation is continuous, and so can be achieved by stretching only without tearing or making new holes in the tori.

A transformation consisting of a constant offset with no rotation or distortion. In n-dimensional Euclidean space, a translation may be specified simply as a vector giving ...

Two submanifolds X and Y in an ambient space M intersect transversally if, for all p in X intersection Y, TX_p+TY_p={v+w:v in TX_p,w in TY_p}=TM_p, where the addition is in ...

A special function psi_1(z) corresponding to a polygamma function psi_n(z) with n=1, given by psi_1(z)=(d^2)/(dz^2)lnGamma(z). (1) An alternative function ...

The trilogarithm Li_3(z), sometimes also denoted L_3, is special case of the polylogarithm Li_n(z) for n=3. Note that the notation Li_3(x) for the trilogarithm is ...

The Tusi couple is a 2-cusped hypocycloid obtained by rolling a circle of radius a inside a circle of radius 2a. The result is a line segment (Steinhaus 1999, p. 145; Kanas ...

A particle P is said to be undergoing uniform circular motion if its radius vector in appropriate coordinates has the form (x(t),y(t),0), where x(t) = Rcos(omegat) (1) y(t) = ...

A web diagram, also called a cobweb plot, is a graph that can be used to visualize successive iterations of a function y=f(x). In particular, the segments of the diagram ...

Whirls are figures constructed by nesting a sequence of polygons (each having the same number of sides), each slightly smaller and rotated relative to the previous one. The ...

Any square matrix T has a canonical form without any need to extend the field of its coefficients. For instance, if the entries of T are rational numbers, then so are the ...