The first computer to calculate Pi

Happy Pi Day! No, that doesn't mean it's time to stuff your face with pasty-based foodstuffs, what it actually refers to is a celebration of the Greek letter of Pi - the symbol that represents the ratio of the circumference of a circle to its diameter. Pi Day is celebrated on 14 March as this is expressed as 3/14 in American style, making it similar to Pi's value of 3.14 correct to two decimal places.

The value of Pi is used in numerous formulae in maths, science and engineering, making it a very important number indeed and one of the most important mathematical constants around, and certainly the most well known. As Pi is what's known as an "irrational" number, it has an infinite number of decimal places, meaning that it never ends, although it's usually written as 3.14159265, or 3.14 in its shortest form.

Naturally, calculating the value of Pi, with its interminable number of decimal places was something of a long-winded process, until the introduction of digital computers in the 20th century. The first example of a computer being to calculate Pi was in 1949, when John von Neumann and chums used ENIAC (Electronic Numerical Integrator And Computer) to compute 2,037 digits of Pi. This room-sized beast of a computer, not unlike Deep Thought from The Hitchhikers' Guide to the Galaxy, took an arduous 70 hours to work out the calculation.

Initially designed to calculate artillery firing tables for the US army, ENIAC was dubbed the "Giant Brain" by the press, when it was first announced in 1946. The ENIAC proudly boasted computing speeds that were claimed to be 1,000 times faster than its electro-mechanical rivals - a mind-boggling large leap in processing power. After a brief shut-down for an upgrade in 1946, the gigantic computer was switched back on in 1947 and ran continuously until it finally logged off in 1955.

Using an IBM card reader for input and an IBM card punch for output, the ENIAC took up slightly more room than the slimline desktop computers of today, weighing around 30 tons and spreading over a massive 63m². Guzzling 150kW of power, it wasn't exactly what we'd call "eco-friendly" either. Along with a staggering 17,468 vacuum tubes, the enormous computer was also home to 70,000 resistors, 10,000 capacitors and 7,200 crystal diodes and was held together with approximately 5 million soldered joints.

The ENICAC was capable of carrying out up to 385 multiplication tasks per second using four of its 20 accumulators, controlled by a multiplier unit. Using five of its accumulators, and a divider/square-rooter unit, it could squeeze out 40 division operations every second or three square root calculations in the same time.

As technology has advanced, the number of digits past the decimal places that can be accurately calculated has grown exponentially, largely thanks to the discovery of the FFT (Fast Fourier Transform) in the 1960s which meant that computers could deal with arithmetic on very large numbers, but at a much speedier pace than had previously been capable. In 2009, French programmer Fabrice Bellard managed to compute Pi to 2,699,999,990,000 decimal places, using a home computer. The entire process, including calculation, conversion and verification took a total of 131 days. This was particularly impressive as Bellard used a single sub-$3000 desktop PC rather than the hugely expensive super-computers that had been used in previous calculations.

In August 2010, a new record was set by Shigeru Kondo who managed to calculate 5,000,000,000,000 digits of Pi, using programmer Alexander Yee's y-cruncher. The calculation was carried out on a home-built computer with the two rounds of verifications taking just 64 and 66 hours to complete.



Over the years, many computer programmes have been written to calculate Pi, with Super PI perhaps being the most famous. This is used by overclocking enthusiasts for benchmarking their computers with world record Pi calculation times, which sounds like possibly the least fun that it's technically possible to have with a computer.

If you're that way inclined, you can even get smartphone apps, such as Calculate Pi which, as the name suggests, will calculate Pi to thousands of decimal places. There are also some apps around where the object of the game is to test yourself and see how many of the decimal places you can remember and recite. Sounds like fun? Perhaps not, but consider your life richer for knowing all of this anyway. Happy Pi Day to you.



>