Tuesday, March 13, 2012

Pi Day is Tomorrow

Tomorrow is a great day, it is an official holiday to celebrate the mathematical constant Pi. Pi is a beautiful thing, it is the constant that represents the ratio of the circle's circumference over its diameter. However, it is so much more then that. There are so many relationships in nature that involve Pi, and tomorrow is a great time to teach the wonder of mathematics to your children.

With that in mind, I felt compelled to share one of the most remarkable pieces of mathematics, Euler's identity.

Pi is one central part of this identity, one of the most beautiful jewels of mathematics. It is a consequence of a more general piece of mathematics, called by the physicist Richard Feynman "one of the most remarkable, almost astounding, formulas in all of mathematics". He was talking about Euler's formula.

Euler's formula describes the connection between algebra and geometry in one simple condensed formula. It relates the complex numbers with the geometry of the triangle, forming a deep connection between two things which to most of us seem separate.

By substituting Pi into Euler's formula, we arrive at Euler's identity.

In Euler's identity three basic arithmetic operations are used exactly once each, addition, multiplication and exponentiation. The identity links 5 fundamental mathematical constants:
• The number Pi, the ratio of the circumference of a circle over its diameter.
• The number e, the base of the natural logarithms.
• The number i, the imaginary unit that allows us to solve any polynomial equation
• The number zero, which is the additive identity
• And finally, the number 1 which is the multiplicative identity.
So much of the foundations of mathematics can be summarized in this tiny little formula. This and countless other relationships in mathematics and nature involve the number Pi. It is so basic and beautiful, it deserves to be celebrated.

So when 3/14 rolls around share a little mathematics with your child on Pi day. Try and show the mathematics around you, bake a round cake or pie, decorate it with some geometric shapes. Teach your children the area formula for a circle by helping them write it on some sugar cookies. There are countless other things you can do with your child, use tomorrow to instill wonder in mathematics. You won't regret it.

You can find plenty of other ideas at the Pi Day official site