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Given a triangle with polygon vertices A, B, and C and points along the sides D, E, and F, a necessary and sufficient condition for the cevians AD, BE, and CF to be ...

Determining the maximum number of pieces in which it is possible to divide a circle for a given number of cuts is called the circle cutting or pancake cutting problem. The ...

A method of computing the determinant of a square matrix due to Charles Dodgson (1866) (who is more famous under his pseudonym Lewis Carroll). The method is useful for hand ...

The most general form of Lagrange's group theorem, also known as Lagrange's lemma, states that for a group G, a subgroup H of G, and a subgroup K of H, (G:K)=(G:H)(H:K), ...

In spherical coordinates, the scale factors are h_r=1, h_theta=rsinphi, h_phi=r, and the separation functions are f_1(r)=r^2, f_2(theta)=1, f_3(phi)=sinphi, giving a Stäckel ...

The lattice method is an alternative to long multiplication for numbers. In this approach, a lattice is first constructed, sized to fit the numbers being multiplied. If we ...

Lehmer's totient problem asks if there exist any composite numbers n such that phi(n)|(n-1), where phi(n) is the totient function? No such numbers are known. However, any ...

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 ...

By asking a small number of innocent-sounding questions about an unknown number, it is possible to reconstruct the number with absolute certainty (assuming that the questions ...

For some authors (e.g., Bourbaki, 1964), the same as principal ideal domain. Most authors, however, do not require the ring to be an integral domain, and define a principal ...