Mathematics
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…]
Articles by OldTrout
Hobbies
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…]
Arts
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
Arts
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…]
Hobbies
The Möbius Function
The Möbius function is denoted by , where is the Greek letter mu. Depending on the factorisation of , the function takes the values . The last says that if is even, then and if [more…]
Hobbies
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…]
Hobbies
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…]
Arts
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…]
Arts
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…]