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The notion of an inverse is used for many types of mathematical constructions. For example, if f:T->S is a function restricted to a domain S and range T in which it is ...

Inversion is the process of transforming points P to a corresponding set of points P^' known as their inverse points. Two points P and P^' are said to be inverses with ...

The geometry resulting from the application of the inversion operation. It can be especially powerful for solving apparently difficult problems such as Steiner's porism and ...

A bijective map between two metric spaces that preserves distances, i.e., d(f(x),f(y))=d(x,y), where f is the map and d(a,b) is the distance function. Isometries are ...

Find a closed plane curve of a given perimeter which encloses the greatest area. The solution is a circle. If the class of curves to be considered is limited to smooth ...

For an algebraic curve, the total number of groups of a g_N^r consisting in a point of multiplicity k_1, one of multiplicity k_2, ..., one of multiplicity k_rho, where sumk_i ...

A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in ...

The Lebesgue measure is an extension of the classical notions of length and area to more complicated sets. Given an open set S=sum_(k)(a_k,b_k) containing disjoint intervals, ...

The line integral of a vector field F(x) on a curve sigma is defined by int_(sigma)F·ds=int_a^bF(sigma(t))·sigma^'(t)dt, (1) where a·b denotes a dot product. In Cartesian ...

A link invariant defined for a two-component oriented link as the sum of +1 crossings and -1 crossing over all crossings between the two links divided by 2. For components ...