## An Eulerian Birthday

A distinctive (I hope) way to mark the occasion of my 41st birthday.

# INTRODUCTION

Today is my birthday, which is the last part of the title explained, so where does the word “Eulerian” come in?

# THE MOST PROLIFIC OF ALL MATHEMATICIANS

For all his immense output Leonhard Euler (pronouned “Oiler”, not “Ewe-ler”) is best known to the world at large for his solution to the “Bridges of Konigsberg” conundrum. Citizens of this then German town (it is now Kaliningrad, Russia) used to amuse themselves by trying to walk around the town crossing each of its seven bridges once and once only in the course of their peregrinations. Nobody ever managed it, and Euler (pioneering the science of topology, a minor offshoot of which is the “Beck Map”, versions of which are now used worldwide as an easy way to display urban public transport routes, in the process) proved that there was no way to do this. This is because each the four landmasses involved contained an odd number of bridgeheads – had specifically two (and it could have been any two), or all four of these landmasses contained even numbers of bridgeheads it would have been possible to devise a walking route using each bridge precisely once.

Much less well known than the above, Euler also noticed that if you feed values into the equation Y = X2 + X + 41 every value of X from 0 through to 39 produces a prime number for Y, and even after the inevitable break to the sequence where X = 40 produces Y = 1681 = 41 * 41, and X = 41 produces Y = 1763 = 41 * 43, the formula continues to produce a very large number of prime numbers – far more than any other formula of similar type. This then is why I described this an Eulerian birthday – it is my 41st. A clue to bear in mind for next year’s birthday is that the person who will play the role in my blog post on that day that Euler has played today was proud of the fact that he was born in Cambridge in 1953 and had initials DNA. More details, including a full listing of the primes produced before X = 40, can be found in Keith Devlin’s “Mathematics: A New Golden Age”.

# PICTURES

I have some pictures, mainly from today at work. These are presented as a ’tiled mosaic’ – click an individual image to view at full size.

# AFTERWORD

Many people on both facebook and twitter have wished my a happy birthday and I thank all of you for so doing – the main celebration, a Sunday lunch at the Crown in East Rudham two days before the actual day was superb.