God Rest Ye Merry, Gentlemen

The words of the carol occur in three broadsides published in Birmingham in the early nineteenth century. An early mention of the carol’s title occurs in William Hone’s 1823 work Ancient Mysteries Described, which includes [more…]

Euclid’s Elements, Book IX, Proposition 20. Theorem : Prime numbers are more than any assigned multitude of prime numbers. That is, there are infinitely many primes. Proof : Suppose that there are primes : Let [more…]

The golden ratio is well known and is associated with the Fibonacci sequence of numbers.     (phi) is the positive root of the quadratic equation . The exact value is given by Its continued [more…]