## A Slice of Mathematical Pi

March 14 is a special day for geeks around the world. It’s**
Pi Day**: the date is 3/14 – the first three digits of the constant ratio between

the circumference of a circle to its diameter, which school kids everywhere know

is approximated to 3.14159.

It also happens to be Einstein’s birthday, so

there’s a double reason to celebrate!

**Why is this Pi Special?**Pi is a very special quantity because it’s what

mathematicians call both an irrational and a transcendental number, which means

it continues infinitely without repetition or pattern. An irrational number is

a real number that cannot be written as a simple fraction. A transcendental number is a real number that is

not the solution of any single-variable polynomial equation whose coefficients are

all integers. All transcendental numbers are irrational numbers but the

converse is not necessarily true: some irrational numbers are not

transcendental numbers.

**How Old is Our Pi?**

For literally thousands of years, mathematicians have

attempted to understand and compute this almost mystical constant. In ancient

times, the famous Greek mathematician and inventor Archimedes of Syracuse and third-century

Chinese mathematician Liu Hui both used geometrical techniques based on

polygons to estimate the value of Pi.

At the time of the Renaissance in Europe and in other parts

of the globe, mathematicians began to develop new algorithms based on infinite

series to compute Pi to new levels of accuracy. Exponents included the 14^{th }century Indian mathematician and astronomer Madhava of Sangamagrama, the

renowned British physicist Sir Isaac Newton, Swiss mathematician and physicist Leonhard

Euler, German scientist Carl Friedrich Gauss, and Indian amateur mathematical

genius Srinivasa Ramanujan.

In more recent times, computer science has greatly added to

our understanding of Pi. Modern computing power has extended its decimal

representation to over 10 trillion or 10^{13} digits. Such accuracy

isn’t really necessary for scientific purposes. Indeed, Jörg Arndt and

Christoph Haenel maintain that a mere 39 digits are sufficient to perform most

cosmological calculations, because that is the accuracy necessary to calculate

the volume of the known universe to the precision of a single atom!

**Geeks Celebrate with Memory Pi**

Nevertheless, calculating Pi to ever higher levels of

accuracy continues to excite the media: as an infinite number, cataloguing π epitomises

the sort of unbounded challenge that appeals to the human spirit; it also

represents a demanding test for the capability of supercomputers and high-precision

multiplication algorithms. This activity has also inspired prodigious feats of

memory from many individuals, with record-holders stretching their recall to over

67,000 digits! The top five are all from Asia – two each from India and Japan –

with the undisputed ‘king of π’ being China’s Lu Chao, who memorised the

constant to 67,890 digits; the following five slots are held by four Brits and

an American.

**Birthday Pi for Einstein!**Ivy League university town Princeton in New Jersey is this

month holding its traditional dual celebrations for Pi Day and Einstein, who lived

there for over 20 years. Among the festivities is an Einstein lookalike

competition, while young geeks are being encouraged to upload their own videos to

celebrate the day. And the prize for the winners? Yup, you guessed it, $314.15!

Did you know? The origins of the phrase ‘squaring the

circle’ lie in the fact that π is a ‘transcendental’ number. This means that it

is impossible to draw to perfection a square with the same area as a given

circle, simply by using a compass and straightedge and following the ancient

Greek rules for geometric constructions. Known as ‘squaring the circle’, this

ancient puzzle has, for centuries, been one of the most baffling challenges in

geometry. Methods have been devised that provide amazingly close approximations

to the problem, but these do not satisfy the instincts of pure mathematicians for

whom estimates are never good enough – a solution is either valid or it isn’t.

How will you be celebrating Pi day and Einstein's birthday in your class?