Going Round in Circles

Or : Multiplying by . The beginning of complex numbers is often attributed to Cardano (1501 – 1576).  Complex numbers provide a solution to the equation . They are an extension of the number system [more…]

The Basel Problem

One sometimes gets very interesting results when one turns divergent sums upside down. The Basel problem was asked by Pietro Mengoli in . He asked what is the exact summation of the reciprocals of the [more…]

Hark! The Herald Angels Sing

Painted in about 1470/75, it is in the National Gallery. One of my favourite carols: Merry Christmas!   OldTrout 2018

Pistachio Ice Cream

Ingredients : 8oz (225g) unsalted, shelled pistachio nuts 1 pint (570ml) double cream 1 pint (570ml) single cream 4oz (110g) golden caster sugar 8 large egg yolks 1 1/2 tablespoons of custard powder   Method [more…]

The Fields Medal

“Rise above oneself and grasp the world” These are awarded every four years for advancement in the field of mathematics.  There is an age limit of 40 on the recipients.  It is a recognition of [more…]

Euler’s Totient Function

Euler’s totient function counts the number of positive integers up to that are relatively prime to , where is considered to be relatively prime to all .  These numbers are called the totatives of . [more…]

The Coventry Carol

Several oil-on-oak-panel versions of The Massacre of the Innocents were painted by 16th-century Netherlandish painters Pieter Bruegel the Elder and his son Pieter Brueghel the Younger. The work translates the Biblical account of the Massacre [more…]

The Holly and the Ivy – King’s College Cambridge 2008

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…]

A Triangle

This is Klauber’s Triangle : – He produced it in the 1930s.  The underlying numbers are the natural numbers ℕ and are arranged as follows : – 1 2   3   4 5   6   7   8   [more…]