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An odd prime p is called a cluster prime if every even positive integer less than p-2 can be written as a difference of two primes q-q^', where q,q^'<=p. The first 23 odd ...

After a half rotation of the coin on the left around the central coin (of the same radius), the coin undergoes a complete rotation. In other words, a coin makes two complete ...

If V and W are Banach spaces and T:V->W is a bounded linear operator, the T is said to be a compact operator if it maps the unit ball of V into a relatively compact subset of ...

Does there exist an algorithm for deciding whether or not a specific mathematical assertion does or does not have a proof? The decision problem is also known as the ...

A surface of constant negative curvature obtained by twisting a pseudosphere and given by the parametric equations x = acosusinv (1) y = asinusinv (2) z = ...

Let G be an algebraic group. G together with the discrete topology is a locally compact group and one may consider the counting measure as a left invariant Haar measure on G. ...

A number of attractive 2-compounds of the regular dodecahedron can be constructed. The first (left figures) has the symmetry of the cube and arises by combining two regular ...

The surface of revolution given by the parametric equations x(u,v) = cosusin(2v) (1) y(u,v) = sinusin(2v) (2) z(u,v) = sinv (3) for u in [0,2pi) and v in [-pi/2,pi/2]. It is ...

The evolute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_e = (a^2-b^2)/acos^3t (3) y_e = (b^2-a^2)/bsin^3t. ...

Let 0<k^2<1. The incomplete elliptic integral of the third kind is then defined as Pi(n;phi,k) = int_0^phi(dtheta)/((1-nsin^2theta)sqrt(1-k^2sin^2theta)) (1) = ...