A slice of Pi

A slice of Pi

SAM JORDISON

TO A CERTAIN type of person, the number 3.14 holds a fascination that can only be equalled by reciting scripts from old episodes of Monty Python or watching repeats of Xena: Warrior Princess. They are the first three digits of pi (p), the key to calculating the circumference and area of every circle. Simply put, it represents the ratio between the diameter and the circumference of any circle, and is one of the most significant numbers in maths. It is also (when it is written in the US fashion) today's date: 3/14.

And that's why maths students at Harvard University are today holding a p recitation contest to see who can list the notoriously long number to the most decimal places. They'll also be holding a pe-eating contest and the naughtier members of the faculty are even threatening to wash those down with some pña colada. Meanwhile, in an attempt to trick their pupils into thinking that maths is fun, teachers all over the world will be bringing pizza p to school and arranging p-themed activities throughout the day. These may or not include the singing of the following beautiful ditty (to the tune of Jingle Bells) written by a teacher and his class in Minnesota especially for the occasion:

Pi day songs

All day long.

Oh, what fun it is,

To sing a jolly pi day song

in a fun math class

like this. (Repeat )

Circles in the snow,

Around and round we go.

How far did we have to run?

Diameter times pi! (Refrain)

I imagine that at this point many of my readers are gagging, if not snorting derisively. Especially since, if you're anything like me, you probably only really know of p as the number that caused you hours of trouble and worry at school when you were instructed to use it to work out the circumference of various circles.

Even now the symbols 2pr send a chill down my spine and until recently I'd never thought to question the importance of all that time spent measuring radii and typing 3.142 into my calculator. The best that I'd have been able to come up with would have been some vague conspiracy theory about keeping Casio and the manufacturers of compasses and protractors in business (and keeping schoolboys like me quiet and unhappy).

I dropped maths as soon as I possibly could, and the vital importance of being able to work with p was lost to me. I hadn't given it any thought for many years. And that's a terrible shame because, as I now know, p really is quite special.

The practical applications of p are, in fact, legion. The number has all kinds of relevances outside the world of square-ruled exercise books and smudged equations, above and beyond the fairly obvious usefulness of being able to accurately work out the circumference of circles in the tunnelling and construction industries. Pi is used in just about every manufacturing process you can think of, from loo rolls to fighter jets. Everywhere there's a circle that needs to be measured, in fact, and that's an awful lot of places, if you think about the number of screws there are in the world (not to mention lenses, tubes and wheels). It's also vital in telecommunications. Radio, TV, telephone and radar signals can all be described as sine waves and p is fundamental in calculating their size and frequency, as it is in calculating the size of the waves in the sea. The magic number is also used in an unutterably complex way to stimulate unknown factors and loading conditions in engineering, wind gusts on a plane, and even random variables in computer-game manufacture.

In short, p is one of the foundation stones of our way of living and we'd be in a lot of trouble without it. It's not overstating things too much to say that the history of our civilisation can be traced in the history of p. Arguably the first technological society, the Babylonians had calculated p using the value of 25/8. It was this level of accuracy that enabled them to produce some of the first serious construction marvels - and to build all those towers that so annoyed the writers of the Old Testament.

Meanwhile, in spite of its claims to be the infallible word of an omnipotent God, the references to p in the Old Testament are distinctly underwhelming. Verses in Kings and II Corinthians about the construction of Solomon's Temple give p a value of "3". Proof at least that the concept had broad currency by the first millennium BC, but nothing like as impressive as the earlier Ancient Egyptian figure of 3.160, written down by a scribe called Ahmes in 1650BC, and which no doubt helped the people of the pharaohs build all those magnificent temples.

The single biggest leap in the evolution of p came, as with so many things, thanks to the ancient Greeks. In the 3rd century BC Archimedes of Syracuse work-ed out the first known theoretical calculation of the number. His idea was that by drawing a polygon outside a circle and then a smaller one inside and calculating the perimeters of both, he'd be able to approximate the circumference of the circle somewhere in between the two figures and thus work his way back to p. This gives a pretty rudimentary value if you draw a four-sided polygon outside and inside the circle, but very accurate when you draw, as Archimedes did, two 96-sided polygons. He worked out the value of p as lying somewhere between 223/71 and 22/7. The average of these two values is roughly 3.1419.

Now, don't worry if you don't completely understand Archimedes's calculations. If I'm being honest, I don't either - which just goes to show how impressive his achievement was. And, just as it took almost two millennia for modern civilisation to catch up with that attained by the ancient Greeks and Romans, it also took almost 2,000 years for Europeans to come up with a better calculation of p. In other words, you aren't alone if you have trouble following the man in the toga. The Indians and Chinese had both produced more accurate approximations by the 15th century AD, but the first modern (ahem) pioneer of Western civilisation was Ludolph van Ceulen, who managed to work the number out to within 35 decimal places. So proud was he of this achievement that he supposedly had them inscribed on his tombstone.

Calculations became steadily more accurate as the Renaissance gave way to the Enlightenment and, in 1706, a Welshman called William Jones also became the first known person to use the actual symbol "p" when discussing the magic number. He did so in a text with the snappy title Synopsis Palmariorium Mathesios. Unfortunately, he didn't record for posterity the reason he opted for this symbol. The best explanation is that it was a little tribute to Archimedes, being the first letter of the Greek word, perimetron, from peri (around) and metrein (to measure). Nobody really knows, but all the same, the symbol stuck, and calculating it accurately became something of a Holy Grail for eggheads around the world as technology advanced during the Age of Steam.

Rather tragically, one William Shanks devoted the 20 years of his life leading up to 1873 to calculating p to 707 decimal places, only to have a DF Ferguson come along in 1944 and prove that his predecessor had made a mistake. Shanks had got the figure at the 528th decimal place wrong, which meant that all his subsequent figures were also incorrect. Ferguson, of course, had a considerable advantage over the Victorian in that he had a mechanical calculating machine, and the development of computers has been tied up with calculations of p ever since. One of the best ways of testing the power of a new machine is still to see how accurately it can work out p - and they now come up with some huge figures. Just over a year ago Professor Kanada at Tokyo University announced the calculation of p to 1.2411 trillion places. If that number were written down from left to right in the same size typeface as this newsprint, it would be long enough to wrap round the Earth.

The other thing that mathematicians came to realise about p as they calculated it more and more accurately is that it's an irrational number. That's to say, you can't get to the end of it if you try and write it down. There will always be more and more numbers to the right of the decimal point - and it can't be described as a fraction, either. The numerical configuration of p is infinite and so, in a particularly mindbending way, as big as the universe.

All of which goes to prove, I hope, why nerds and mathematicians get so excited about the 14th day of the third month, and why they have adopted it as their own special day of celebration, just as romantics have Valentine's Day, batter-lovers have Pancake Day, and Mums have Mother's Day (don't forget, by the way, it's this Sunday). It's easy to mock those pasty students drinking piña colada, reciting huge numbers to each other and dancing to Don Maclean's American Pie, but when you think about it, they're closer than any of us to understanding one of the secrets of the cosmos. If that isn't cause for celebration, I don't know what is.

THE SECRET LIFE OF p

1 THERE'S some controversy over the exact time celebrations of p day should begin. Some state that 1:59pm is the best time, but those who prefer the 24-hour clock say you should go for 1:59 in the morning as 1:59pm is represented on a 24-hour clock as 15:59.

2 On Kate Bush's double album Aerial, there is a song called p. In it Bush recites the number to its 137th decimal place, inexplicably omitting the 37th and 100th places.

3.1415... The European record for recounting p belongs to Daniel Tammet, who recited the number to its 22,514th digit on 14 March 2004.

4 As well as being p day, 14 March was also the birthday of Albert Einstein.

5 Lars Erickson, a mathematician and composer, has written an entire symphony based on p.

6 Even though computers have worked out a value of p to billions of decimal places, it's very rare that such accuracy is needed. For instance, working out the circumference of the Earth's equator from its radius using only ten decimal places of p produces an error of less than 0.2 millimetres. Not bad, out of 40,075.02 km.

7 Here's p to 50 decimal places: 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510

8 In The Simpsons' episode "Marge in Chains", Apu boasts that he can recite p to 40,000 decimal places. When asked what the 40,000th number is, he answers "one", which is quite correct. Rumour has it that the script writers approached the mathematician David H Bailey in order to get it right.

This article: http://news.scotsman.com/scitech.cfm?id=398332007

Last updated: 14-Mar-07 01:34 GMT

musicismylife / 6:22am 14 Mar 2007

It seems my husband, Scaramouche, is STILL being moderated against and his posts disallowed. I'd like to know how he's been so bad compared with some of the posts I've seen on this forum.
Anyway, he's asked me to submit his Ode to Math for the delectation of his public. (silly old f*rt!!)

Flat
Like an angle in a triangle
A plane upon a plane
Euclidian geometry's
Not too hard to explain
Like a pi rolls down a mountain
Or a path upon a sphere
Once you hit that third dimension
It all becomes less clear
Like a tiny 1-D superstring
That's infinitely small
It exists in ten dimensions,
Or is it really there at all?
These are problems that you face
When pondering n-dimensional space

Like a tesseract unfolding
As from nowhere it has grown
We see it coming from a fourth
Dimension of its own
Like a door that keeps revolving
Pushed by Schroedinger's dead cat
Just which three of the ten
Dimensions are we looking at?
Like a theory mutated
On a plane that's rearranged
And topology that's twisted
'Till reality has changed
Can mathematics keep apace
With changing N-dimensional space?

Sets that hold dimensions
Whose dimensions set the sets
If you understand recursion
That's as complex as it gets
Things that by their interactions
And their intersects defined
Does the logical conclusion cause
Implosion of the mind?
Pictures like they were by Dali
Looking really, very odd
In the depths of quantum physics
Do we see the face of God?
When you knew exams were over
Were you suddenly aware
That what you wrote was rubbish
But now you really couldn't care .....

Like a one-dimensional ribbon
Like a thread around a thread
Superstring theory turns
The world upon its head
And it shows a certain grace
Electro-microscopic lace
In N-Dimensional space

*adapted from "Windmills of Your Mind" by Noel Harrison

Musicismylife / 8:44pm 14 Mar 2007

Scaramouche is still not being allowed to post. He's spitting nails!!! Silly old duffer better not have another heart attack, or I'll be at the Scotsman door screaming blue bloody murder!

Anyway, he wants me to point out that it's not a poem it's a SONG. It was featured in the 1968 Steve McQueen movie The Thomas Crown Affair. Director Norman Jewison wanted a song that sounded like The Beatles "Strawberry Fields Forever" for a scene where McQueen's character is flying a glider. The song provided a contrast to the visual ..... McQueen appeared firmly in control, but the music made viewers feel the trepidation going through his mind.
Songwriters Michel Legrand and Marilyn and Alan Bergman wrote it. It took them a while to come up with the title, which they chose because they thought it was interesting.
The song won the 1969 Oscar for Best Song From A Film. It was sung by Noel Harris Harrison, the son of the British actor Rex Harrison. He is best known in the US for co-starring with Stefanie Powers in the popular '60s TV spy series The Girl From U.N.C.L.E.
Dusty Springfield recorded a popular version of this song on her 1969 album Dusty In Memphis.
Edward Woodward also recorded a rather disturbing version of this song on his 1972 album 'The Edward Woodward Album' (now sadly hard to find, but comparable, in places, to William Shatner's 'musical' work from the same period).
Alison Moyet has also recorded this song on her album "Voices". It is very mellow, quite soft-jazzy and being that Alison Moyet has quite a low, husky voice means that like "Only You" from her days with Yazoo.
Noel Harrison's also recorded "A Young Girl" .... originally sung (in French) by Edith Piaf as "Une Enfant".
Jose Feliciano sang the song at the Academy Award show because Harrison was busy making a movie and the director would not let him fly to Hollywood to sing it.
Noel Harrison hosted the TV show Hullabaloo. He had a parking space at MGM next to Natalie Wood. He toured for a while with The Beach Boys and Sonny and Cher.
In the 1970's Harrison fled Hollywood following his stint as Mark Slate on The Girl From U.N.C.L.E. He went to Nova Scotia, grew a bushy beard, and built a house with no electricity. The wood stove caused it to burn to the ground and he had to rebuild it from scratch. To go Back click here.