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The use of permil (a.k.a. parts per thousand) is a way of expressing ratios in terms of whole numbers. Given a ratio or fraction, it is converted to a permil-age by ...

Catalan's triangle is the number triangle 1 ; 1 1 ; 1 2 2 ; 1 3 5 5 ; 1 4 9 14 14 ; 1 5 14 28 42 42 ; 1 6 20 48 90 132 132 (1) (OEIS A009766) with entries given by ...

A planar polygon is convex if it contains all the line segments connecting any pair of its points. Thus, for example, a regular pentagon is convex (left figure), while an ...

A law is a mathematical statement which always holds true. Whereas "laws" in physics are generally experimental observations backed up by theoretical underpinning, laws in ...

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 repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats ...

The position of a rational number in the sequence 1/1, 1/2, 2/1, 1/3, 3/1, 1/4, 2/3, 3/2, 4/1, 1/5, ..., ordered in terms of increasing numerator+denominator.

Division by zero is the operation of taking the quotient of any number x and 0, i.e., x/0. The uniqueness of division breaks down when dividing by zero, since the product ...

The unique even prime number 2. All other primes are odd primes. Humorously, that means 2 is the "oddest" prime of all. The sequence 2, 4, 6, 10, 14, 22, 26, 34, 38, ... ...

There are several results known as the Morgado identity. The first is (1) where F_n is a Fibonacci number and L_n is a Lucas number (Morgado 1987, Dujella 1995). A second ...