Problem All square roots are periodic when written as continued fractions and can be written in the form: For example, let us consider ?23: If we continue we would get the following expansion: The process can be summarised as follows: It can be seen that the sequence is repeating. For conciseness, we use the notation [...]

Problem It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square roots is infinite without any repeating pattern at all. The square root of two is 1.41421356237309504880…, and the digital sum of the first one hundred decimal digits [...]

Problem Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae: The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties. The set is cyclic, in that the last two digits of each number is the first two digits of the [...]

Well, last year’s F# tour was so much fun, I figured I would try to do it again, in Europe this time. I am becoming quite fond of F# tourism: after all, what better way to discover a place than going there and meeting locals who happen to have at least one common interest – and spread the F# love in the process? Anyways, if everything goes according to plan, I should be visiting F# communities in 7 different countries in 6 weeks :) As an aside, if you are running a meetup/user group that is somewhat on my[...]

Bit Syntax in Erlang One of the often under-appreciated features of Erlang is its Bit Syntax for parsing and pattern matching binary data at a bit level. For instance, to pare TCP segments you can write something along the line of: The same capability can be applied to anything binary protocols, such as video encoding, [...]