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The salinon is the figure illustrated above formed from four connected semicircles. The word salinon is Greek for "salt cellar," which the figure resembles. If the radius of ...

The smallest positive composite number and the first even perfect square. Four is the smallest even number appearing in a Pythagorean triple: 3, 4, 5. In the numerology of ...

The Lucas-Lehmer test is an efficient deterministic primality test for determining if a Mersenne number M_n is prime. Since it is known that Mersenne numbers can only be ...

3 is the only integer which is the sum of the preceding positive integers (1+2=3) and the only number which is the sum of the factorials of the preceding positive integers ...

Find the plane lamina of least area A which is capable of covering any plane figure of unit generalized diameter. A unit circle is too small, but a hexagon circumscribed on ...

In a given acute triangle DeltaABC, find the inscribed triangle whose perimeter is as small as possible. The answer is the orthic triangle of DeltaABC. The problem was ...

A convex figure constructed by iteratively halving the base of an equilateral triangle and then sliding adjacent triangles so that they slightly overlap. Combining several ...

A curve which may pass through any region of three-dimensional space, as contrasted to a plane curve which must lie in a single plane. Von Staudt (1847) classified space ...

1729 is sometimes called the Hardy-Ramanujan number. It is the smallest taxicab number, i.e., the smallest number which can be expressed as the sum of two cubes in two ...

A weak snark is a cyclically 4-edge connected cubic graph with edge chromatic number 4 and girth at least 4 (Brinkmann et al. 2013). Weak snarks therefore represent a more ...