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A bubble is a minimal-energy surface of the type that is formed by soap film. The simplest bubble is a single sphere, illustrated above (courtesy of J. M. Sullivan). More ...

There are two definitions of the Carmichael function. One is the reduced totient function (also called the least universal exponent function), defined as the smallest integer ...

The "Cartesian ovals," sometimes also known as the Cartesian curve or oval of Descartes, are the quartic curve consisting of two ovals. They were first studied by Descartes ...

"Casting out nines" is an elementary check of a multiplication which makes use of the congruence 10^n=1 (mod 9). Let decimal numbers be written a=a_n...a_2a_1a_0, ...

Catalan (1876, 1891) noted that the sequence of Mersenne numbers 2^2-1=3, 2^3-1=7, and 2^7-1=127, and (OEIS A007013) were all prime (Dickson 2005, p. 22). Therefore, the ...

A problem sometimes known as Moser's circle problem asks to determine the number of pieces into which a circle is divided if n points on its circumference are joined by ...

A prime number p is called circular if it remains prime after any cyclic permutation of its digits. An example in base-10 is 1,193 because 1,931, 9,311, and 3,119 are all ...

A series is said to be conditionally convergent iff it is convergent, the series of its positive terms diverges to positive infinity, and the series of its negative terms ...

The constant lambda=1.303577269034296... (OEIS A014715) giving the asymptotic rate of growth Clambda^n of the number of digits in the nth term of the look and say sequence, ...

A closed box composed of three pairs of rectangular faces placed opposite each other and joined at right angles to each other, also known as a rectangular parallelepiped. The ...