The delights of numbers

At university I decided to take a maths course one semester, just to prove I could do it - I'd been a little spooked by maths in high school. It turned out to be a really enjoyable experience, especially as I got a lot of help from this really nice guy ... but that's another story...

Since then, I've forgotten how to do quadratic equations (never mind calculus etc), and completely failed to grasp the way my son was taught maths in junior school. Although I never want to encounter another math problem on an exam, I've been interested in mathematical ideas and history, in a minor sort of way. It helps that Mr.T. (or rather, Dr.T.) knows lots of physics and, having been a teacher, can patiently explain equations and suchlike as the need arises, eg at a fascinating exhibition at Fondation Cartier in Paris in 2011 called Mathematics: A Beautiful Elsewhere.

He recommended I read this article in the weekend paper, and I am passing on the recommendation. By Simon Singh, it's about how the writers for The Simpsons, many of whom are mathematicians [go figure...], slipped a lot of maths into the show, often but not exclusively as freeze-frame gags, which fly by unnoticed during normal viewing but, paused on playback, offer delights to the cognoscenti.

These figures from a 2006 episode delight maths buffs by representing a perfect number (8128 is the fourth in the list of perfect numbers), a narcissistic number (of which fewer than 100 exist), and a special kind of prime number, named after the 17th century French monk who spotted it.

Coincidentally, last week More or Less on Radio 4 made much of happy numbers, which are much more numerous than, and not to be confused with, perfect numbers. The smallest happy number is 1, because the sum of the square of its digits adds up to 1. As does the sum of the square of the digits of 103 (a happy prime) - 1x1=1 plus 0x0=0 plus 3x3=9 equals 10, then taking the squares of those digits 1x1=1 plus 0x0=0 equals 1.

And what about magic squares? Intriguing, or what! And you can get lots of addition practice with them... This famous one is from Durer's 1514 engraving "Melancholia" -

Back to the article about the Simpsons - it includes the derivation of "Google" - it's a common misspelling of googol, a term suggested by a nine year old for the number 10 to the power of 100 - ie, 1 with 100 zeros after it - a biggish number - and the little boy went on to suggest "googolplex" for an even larger googol. The Google name of the search engine implies that it provides access to vast amounts of information ... which it does...

Finally, if you missed it in the printed article (it's at the end of the online version), a mind-boggling piece of legislative history, written so well that it would be a travesty to paraphrase. It starts by reminding us that pi is an irrational number (its digits go on an on, not repeating the sequence), 3.14159265...

"The Indiana Pi Bill was the brainchild of Edwin J Goodwin, a physician from the town of Solitude in the south-western corner of the state. He had approached the assembly and proposed a bill that focused on his solution to a problem known as "squaring the circle". He seemed oblivious to the fact that this ancient problem had already been proved impossible in 1882. Goodwin's complicated and contradictory "solution" effectively dictated a value for π equal to 3.2. He said that Indiana schools could use his discovery without charge, but that the state and he would share the profits from royalties charged to other schools who wished to adopt a value of 3.2 for π.

Initially, the technical nature of the bill baffled the politicians, who then passed it without any objection. It was then up to the state senate to ratify the bill.

Fortunately, Professor CA Waldo, a mathematician at Indiana's Purdue University, alerted senior politicians to the absurd legislation. This prompted Senator Orrin Hubbell to proclaim: "The Senate might as well try to legislate water to run uphill as to establish mathematical truth by law."

There was a successful motion to indefinitely postpone the passing of the bill, but it still exists in a filing cabinet in the basement of the Indiana statehouse, waiting for a gullible politician to resuscitate it."