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The largest unit fraction, 1/2. 1/2 is a rational number with terminating decimal expansion 0.5.

A basis for the real numbers R, considered as a vector space over the rationals Q, i.e., a set of real numbers {U_alpha} such that every real number beta has a unique ...

A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in R and all the Q_p, then the equations have solutions in the ...

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 ...

An irreducible fraction is a fraction p/q for which GCD(p,q)=1, i.e., p and q are relatively prime. For example, in the complex plane, (4+7i)/(2+i)=3+2i is reducible, while ...

A rational homomorphism phi:G->G^' defined over a field is called an isogeny when dimG=dimG^'. Two groups G and G^' are then called isogenous if there exists a third group ...

The conjecture that the Artin L-function of any n-dimensional complex representation of the Galois group of a finite extension of the rational numbers Q is an Artin ...

A lens space L(p,q) is the 3-manifold obtained by gluing the boundaries of two solid tori together such that the meridian of the first goes to a (p,q)-curve on the second, ...

A subset M of a Hilbert space H is a linear manifold if it is closed under addition of vectors and scalar multiplication.

The winding number W(theta) of a map f(theta) with initial value theta is defined by W(theta)=lim_(n->infty)(f^n(theta)-theta)/n, which represents the average increase in the ...