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An algebraic identity is a mathematical identity involving algebraic functions. Examples include the Euler four-square identity, Fibonacci identity, Lebesgue identity, and ...

Given a geodesic triangle (a triangle formed by the arcs of three geodesics on a smooth surface), int_(ABC)Kda=A+B+C-pi. Given the Euler characteristic chi, intintKda=2pichi, ...

A necessary and sufficient condition for a curve to be a helix is that the ratio of curvature to torsion be constant.

The functional derivative is a generalization of the usual derivative that arises in the calculus of variations. In a functional derivative, instead of differentiating a ...

A theorem, also known as Bachet's conjecture, which Bachet inferred from a lack of a necessary condition being stated by Diophantus. It states that every positive integer can ...

The quantities obtained from cubic, hexagonal, etc., lattice sums, evaluated at s=1, are called Madelung constants. For cubic lattice sums ...

Consider Kimberling centers X_(20) (de Longchamps point Z; intersection L_S intersection L_E of the Soddy line and Euler line), X_(468) (intersection L_E intersection L_O of ...

A polynomial admitting a multiplicative inverse. In the polynomial ring R[x], where R is an integral domain, the invertible polynomials are precisely the constant polynomials ...

A transformation in which the coordinate system is changed, leaving vectors in the original coordinate system "fixed" while changing their representation in the new ...

If X is any space, then there is a CW-complex Y and a map f:Y->X inducing isomorphisms on all homotopy, homology, and cohomology groups.