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.

Trials and Tribulations

An account of recent events at James and Sons.

INTRODUCTION

Yesterday was James and Sons’ May auction, at Fakenham Racecourse, and today we had a badge sale at our shop in Fakenham.

WEDNESDAY

Our main auction was blighted by problems with the internet connection at the venue. Eventually we relocated the auction itself to Cool Roxy, the owners and trainers bar, while leaving the stock in the Prince of Wales Suite. This left us way behind schedule. Nevertheless, the sale was very successful, with five pieces of postcard artwork accompanied by sample postcards by a man called Twelvetrees selling phenomenally well, some old vinyl records selling well (a Black Sabbath recording went for £340), and many other items faring well. Among the lesser lights a book of photographs from King’s Lynn’s past went for just £4 (it goes well with my substantial digital archive of pictures from King’s Lynn’s present thank you), while a Cornwall Polytechnic Society medallion featuring a bust of James Watt (he after whom the unit of power is named, and who along with his distant predecessor Heron of Alexandria, his closer predecessor Thomas Newcomen and his near contemporary Richard Trevithick played a key role in the development of the steam engine, the first power source for locomotives) went for £11. In amongst all this I had to get images of the reverse sides of the some of the badges being sold today to resolve queries.

Overall, the early problems not withstanding it was a successful day, and here are some photos…

TODAY

Today’s sale proceeded smoothly. Although no huge prices were recorded a number of items did better than expected. Overall therefore I think we can say it was a successful week, although very draining (especially yesterday).