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The Machin-like formula 1/4pi=12cot^(-1)18+8cot^(-1)57-5cot^(-1)239.

The transform inverting the sequence g(n)=sum_(d|n)f(d) (1) into f(n)=sum_(d|n)mu(d)g(n/d), (2) where the sums are over all possible integers d that divide n and mu(d) is the ...

The cubic formula is the closed-form solution for a cubic equation, i.e., the roots of a cubic polynomial. A general cubic equation is of the form z^3+a_2z^2+a_1z+a_0=0 (1) ...

The Gauss-Bonnet formula has several formulations. The simplest one expresses the total Gaussian curvature of an embedded triangle in terms of the total geodesic curvature of ...

Gauss's forward formula is f_p=f_0+pdelta_(1/2)+G_2delta_0^2+G_3delta_(1/2)^3+G_4delta_0^4+G_5delta_(1/2)^5+..., (1) for p in [0,1], where delta is the central difference and ...

Newton's forward difference formula is a finite difference identity giving an interpolated value between tabulated points {f_p} in terms of the first value f_0 and the powers ...

A partial differential equation which appears in differential geometry and relativistic field theory. Its name is a wordplay on its similar form to the Klein-Gordon equation. ...

An example of a subspace of the Euclidean plane that is connected but not pathwise-connected with respect to the relative topology. It is formed by the ray y=0, x<=0 and the ...

Using a Chebyshev polynomial of the first kind T(x), define c_j = 2/Nsum_(k=1)^(N)f(x_k)T_j(x_k) (1) = 2/Nsum_(k=1)^(N)f[cos{(pi(k-1/2))/N}]cos{(pij(k-1/2))/N}. (2) Then f(x) ...

J. Tupper concocted the amazing formula 1/2<|_mod(|_y/(17)_|2^(-17|_x_|-mod(|_y_|,17)),2)_|, where |_x_| is the floor function and mod(b,m) is the mod function, which, when ...