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Transfinite induction, like regular induction, is used to show a property P(n) holds for all numbers n. The essential difference is that regular induction is restricted to ...

Inference of the truth of an unknown result obtained by noting its similarity to a result already known to be true. In the hands of a skilled mathematician, analogy can be a ...

A requirement necessary for a given statement or theorem to hold. Also called a condition.

The Machin-like formula 1/4pi=2cot^(-1)(2)-cot^(-1)(7). The other 2-term Machin-like formulas are Euler's Machin-like formula, Hutton's formula, and Machin's formula.

The Machin-like formula 1/4pi=2cot^(-1)(3)+cot^(-1)(7). The other two-term Machin-like formulas are Euler's Machin-like formula, Hermann's formula, and Machin's formula.

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 geodesic triangle with oriented boundary yields a curve which is piecewise differentiable. Furthermore, the tangent vector varies continuously at all but the three corner ...

If xsinalpha=sin(2beta-alpha), then (1+x)int_0^alpha(dphi)/(sqrt(1-x^2sin^2phi))=2int_0^beta(dphi)/(sqrt(1-(4x)/((1+x)^2)sin^2phi)).

For an arbitrary not identically constant polynomial, the zeros of its derivatives lie in the smallest convex polygon containing the zeros of the original polynomial.

The index of a vector field with finitely many zeros on a compact, oriented manifold is the same as the Euler characteristic of the manifold.