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A curve named and studied by Newton in 1701 and contained in his classification of cubic curves. It had been studied earlier by L'Hospital and Huygens in 1692 (MacTutor ...

Take the Helmholtz differential equation del ^2F+k^2F=0 (1) in spherical coordinates. This is just Laplace's equation in spherical coordinates with an additional term, (2) ...

Let G be a permutation group on a set Omega and x be an element of Omega. Then G_x={g in G:g(x)=x} (1) is called the stabilizer of x and consists of all the permutations of G ...

A surface which can be interpreted as a self-intersecting rectangle in three dimensions. The Whitney umbrella is the only stable singularity of mappings from R^2 to R^3. It ...

If 1<=b<a and (a,b)=1 (i.e., a and b are relatively prime), then a^n-b^n has at least one primitive prime factor with the following two possible exceptions: 1. 2^6-1^6. 2. ...

cos(pi/(12)) = 1/4(sqrt(6)+sqrt(2)) (1) cos((5pi)/(12)) = 1/4(sqrt(6)-sqrt(2)) (2) cot(pi/(12)) = 2+sqrt(3) (3) cot((5pi)/(12)) = 2-sqrt(3) (4) csc(pi/(12)) = sqrt(6)+sqrt(2) ...

A set-theoretic term having a number of different meanings. Fraenkel (1953, p. 37) used the term as a synonym for "finite set." However, according to Russell's definition ...

Order the natural numbers as follows: Now let F be a continuous function from the reals to the reals and suppose p≺q in the above ordering. Then if F has a point of least ...

The Pell-Lucas polynomials Q(x) are the w-polynomials generated by the Lucas polynomial sequence using the generator p(x)=2x, q(x)=1. The first few are Q_1(x) = 2x (1) Q_2(x) ...

Pythagoras's constant sqrt(2) has decimal expansion sqrt(2)=1.4142135623... (OEIS A000129), It was computed to 2000000000050 decimal digits by A. J. Yee on Feb. 9, 2012. The ...