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You can have your pi and eat it, on Pi Approximation Day (22/7)!

Today is 22/7. No prizes for guessing what that means – yes, its Pi Approximation Day! March 14th (3.14) is also celebrated as Pi Day, but I kind of prefer the 22/7 version.

Pi, that curious little number that seems to pop up every time we start going in circles. A number so important that it even got its own name – not many numbers can claim that distinction!

Instead of going in circles trying to figure out what to give the kids for lunch, take your cue from the date and bake them a pi!
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Pi, or π, is a mathematical constant that represents the ratio between a circle’s circumference and its diameter, or π = C/d. It is what’s known as an irrational number – a number that cannot be expressed as a ratio between two integers. Being irrational, it has an infinite number of digits in its decimal representation, and it does not end with a repeating sequence of digits. It is also a trancendental number – a number that cannot be expressed with a finite sequence of algebraic operations.

In addition to its application in geometry and trigonometry, the constant π is found in many formulae, in a variety of sciences, including physics, number theory, thermodynamics, statistics, electromagnetism and mechanics.

The value of π (to 5 decimal places) is 3.14159, which is also approximately the value of 22 divided by 7. Calculating the value of π to higher and higher degrees of accuracy have been a challenge to mathematicians and computer scientists through the ages. Utilising the latest computing technology, the digital representation of π has now been calculated to more than 10 trillion digits. Memorising π to a large number of digits (a practice called piphology) is another challenge taken up by many pi-fanatics, and the current record stands at an astounding 67 890 digits, recited in 2005 in China by Lu Chao over a period of more than 24 hours. (Wow, he probably doesn’t get out much!)

A nice trick to remember the first few digits of pi is to use a poem or sentence where the lengths of the words correspond to the digits in pi. A well-known example, courtesy of English scientist James Jeans, is “How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics”, cleverly representing pi’s first 15 digits.

Such is the pervasiveness of the number π that it can even boast numerous appearances in modern popular culture, from TV series (Simpsons, Twin Peaks) to novels (Carl Sagan’s “Contact”) to pop music (Kate Bush’s “Pi“).

Party like a mathematician on Yellow Pig Day!

17 July is not just another ordinary day; just like a yellow pig is not just another ordinary pig. Today is Yellow Pig Day, the day to take a moment to honour the magical, mathematic pig that has inspired mathematicians for years.

The yellow pig was invented in the early 60’s by two Princeton maths students, Michael Spivak and David C. Kelly, while working on an assignment to identify unique properties of the number 17. After some intense mental gymnastics (and possibly a few pints at the local pub), when they finally ran out of ideas, they thought up the yellow pig, a mythical 17-eyelashed creature (that’s eight lashes on one eye and nine on the other, of course).

OK, so Winnie the Pooh’s friend Piglet is generally considered to be pink, but look closely, and you may notice him turning yellow for just one day of the year…
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Spivak has since written a number of mathematics textbooks, where he regularly includes hidden references to yellow pigs, while David Kelly presents an annual mathematics summer school to high school students, where he introduces them to the “Cult of the Yellow Pig”.  He is rumoured to be the proud owner of an impressive collection of between 289 (17 squared) and 4913 (17 cubed) yellow pigs. When asked about the significance of a yellow pig, he responds, “If you have to ask, you just won’t understand.”

Through Spivak and Kelly’s efforts, yellow pigs have become popular toys among mathematicians. Yellow Pig Day is also celebrated at various (mainly US) University Maths Departments, with the singing of yellow pig carols and the eating of yellow pig cake.

By the way, if you’re unsure about the significance of the number 17, look no further than this list. There’s no doubt the number is as special and magical as the yellow pig itself…

World Music Day with a jolt of Maths

World Music Day is the brainchild of American musician Joel Cohen, who first proposed the idea in France in 1976, while working at a French radio station.  His idea – an all night festival of free music on summer solstice – won favour with the French Minister of Culture, and the first Fête de la Musique took place in 1982.

Now in its 30th year, the celebration has grown into a huge international celebration of free music.  On 21 June, musicians the world over take to the streets and share their art in public spaces, shop-fronts and side-streets to create a beautiful global noise – the only ‘rule’ being that the performances should be free of charge.

Keep on rockin’ in the free world!
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If you’re scientifically inclined, of course, a global celebration of music also happens to be a celebration of mathematics. Yes indeed, when you celebrate the beauty and emotion inherent in music, you are also acknowledging the beauty of mathematical theory and logic.

Simply speaking, rhythm, musical notes and chords can all be explained mathematically, defined in terms of numerical patterns, scales and equations. At a deeper level, composers are often drawn (consciously or not) to mathematical structures – Bach made use of mathematical symmetry, Debussy employed fibonacci number sequences, Erik Satie used the golden ratio in several of his compositions, and many more. Complex, atypical rhythmic structures, as employed in the work of modern minimalist composers like John Cage and Steve Reich, has found favour in a modern rock music sub-genre known as math-rock, where musicians employ complex rhythms, odd, asymmetrical time signatures, angular melodies and dissonant chords.

Where there is music, mathematics is never far away.  In the words of Igor Stravinsky, “Mathematics swims seductively just below the surface.”

So when you’re out enjoying your free musical fix on World Music Day, you may just get a little jolt of maths in the process – enjoy it!

Music = Mathematics + Magic
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Happy Birthday to Donald, the Mathmagical Duck

On this day back in 1934, the world was introduced for the first time to Donald Fauntleroy Duck, when he made his first appearance in the cartoon “The Wise Little Hen”.  The excitable, short-tempered but lovable duck went on to become one of the world’s favourite cartoon characters, and the de facto mascot for The Walt Disney Company.

So what does this have to do with science, you may ask?  Well, Donald Duck often appeared in cartoons touching on traditionally non-cartoony subjects like politics, religion and, yes, science and mathematics.

Donald Duck is no stranger to the magical world of mathematics
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In the 1959 cartoon “Donald in Mathmagic Land“, Donald accidentally stumbles into a magical land of mathematics – a land where trees have square roots, streams are filled with numbers, and a geometric bird recites the digits of Pi.

In the cartoon, Donald is shown that mathematics is not just for eggheads (his original opinion) and that it’s actually useful and even exciting.  He meets, and plays some music with, Pythagoras and his secret band of Pythagorians, where he discovers that mathematics form the basis of musical scales.  From Pythagoras he also receives a pentagram, through which he goes on to learn about the golden section and the golden rectangle, and how these appear in architecture (the Parthenon, etc) and art, such as the Mona Lisa.

Donald discovers that the golden section also shows itself in the human body and in nature, in flowers, plants and shells.  He learns that mathematics even applies to sports and games, such as chess, baseball, basketball and billiards.

A cool bit of intertextuality in the cartoon comes through the inclusion of some themes from “Through the Looking Glass” by Lewis Carroll, who was himself also a mathematician.

In this cartoon Donald Duck, and with him millions of children, are introduced to the wonders of mathematics in a fun and humorous way, and the cartoon closes with the wonderful Galileo quote:
“Mathematics is the alphabet with which God has written the universe”.

Here’s to you, Donald – Happy Birthday, you grumpy old duck!

Fascination of Plants Day

So today, 18 May 2012, is the first ever official “Fascination of Plants Day”, launched under the umbrella of the European Plant Science Organisation (EPSO).

In a way it is sad that there’s a need for an official day to get us humans to appreciate the many wonders of plants and the natural world around us. Expounding at length on the virtues of plants would fill volumes, so I’ll just touch on one aspect that leaves me forever fascinated.

Mathematical marvels

A feast of Fibonacci – this marguerite daisy flaunts its mathematical side by not only sporting 21 petals (a Fibonacci number), but also displaying some intricate Fibonacci spirals in the flower head.
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Plants are truly the physical embodiment of mathematical precision.  The more time we devote to the study of the mathematical structure of our flora, the more fascinating it becomes.  Ferns curve according to the golden section, fibonacci numbers appear all over the place, in the patterns of leaves, the number of petals on flowers, and the wonderfully intricate spirals appearing on flower heads. Then there’s the uncanny fractal structures created by veins of leaves, and beautifully displayed on the broccoflower.

So go on, spend some time in the garden – its good for you, not just physically, but mentally as well!

The lovely little Manuka flower. Not only does it provide another lesson in fibonacci numbers, with 1 stigma, 5 petals, 5 sepals and and 21 anthers, but its also a little medical miracle, source of an abundance of naturally-occuring antibacterial and anti-fungal constituents.
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Natural fractal patterns in the broccoflower.
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Even a garden thistle is a marvel of mathematical structure.
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