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Relates evolutes to single paths in the calculus of variations. Proved in the general case by Darboux and Zermelo in 1894 and Kneser in 1898. It states: "When a single ...

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

Let D be a planar Abelian difference set and t be any divisor of n. Then t is a numerical multiplier of D, where a multiplier is defined as an automorphism alpha of a group G ...

Let t be an infinite word over a finite alphabet Sigma. Then there exists a uniformly recurrent infinite word r such that Sub(r) subset= Sub(t), where Sub(w) is the set of ...

An algebraic equation is algebraically solvable iff its group is solvable. In order that an irreducible equation of prime degree be solvable by radicals, it is necessary and ...

There exists a system of distinct representatives for a family of sets S_1, S_2, ..., S_m iff the union of any k of these sets contains at least k elements for all k from 1 ...

Every modular system has a modular system basis consisting of a finite number of polynomials. Stated another way, for every order n there exists a nonsingular curve with the ...

On a compact oriented Finsler manifold without boundary, every cohomology class has a unique harmonic representation. The dimension of the space of all harmonic forms of ...

The necessary and sufficient condition that an algebraic curve has an algebraic involute is that the arc length is a two-valued algebraic function of the coordinates of the ...

If f_1,...,f_m:R^n->R are exponential polynomials, then {x in R^n:f_1(x)=...f_n(x)=0} has finitely many connected components.