A Slice of Mathematical Pi

It's Pi Day!

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!

 

 



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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 14th 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 1013 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.

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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?  

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