π Revisited

While walking around in a store, I saw a symbol that usually only appears in a textbook. It is π.

It is some cologne with that name. Not sure it is named that way, and I didn't bother to ask for a long strip of paper for a smell. I am tempted to make a lucky star or a Mobius Strip out of those.

Ask some people... just what IS π (in math)? The unfortunate uneducated will have no clue. For those who know, ah ha, it is a trap. If the person starts with "It IS 3.14..." then this person can never finish because no amount of digits can fully spell out π. Better: it is the ratio of circumference over diameter, or it is approximately 3.14...

When I was an elementary school student, the symbol π is an odd ball to me.
Question 1: where did the value come from? (My guess was a very precise ruler to take such measurement of C/d)
Question 2: Why do we use a Greek symbol?

Well I didn't seek answers very hard back then. But the answers has to do with the great Greek mathematician Archimedes. π is actually an abbreviation, it was the first letter of Greek word that means "perimeter". Waita minute, perimeter? Yes, π is the perimeter of a circle with diameter of 1.

Archimedes uses a very interesting "trap" trick to estimate the value of π. He starts with a circle of radius = 1. What's the area? yes, it is π. He used regular polygons and circumscribed polygons to set that upper and lower limit! See this illustration. This legacy should be taught in high school geometry class (but I wasn't informed).

Mathematicans loves the Greek alphabet. π is used in other places... you may remember the product of a sequence with capital Pi...

One other use I know of... to denote the prime counting function, number of primes less than some number x as π(x).

Wiki has so much nicely presented knowledge. It is a treasure chest.

High school geometry class probably should include a writing assignment: about π, about e, about the imaginary number i, or about the golden ratio φ. Extra Credit: How about writing connect e,i,π with the "dazzling"* Euler Formula. Write about it, derive it... Math is so much more than calculations.

That cologne... targeting math enthusiasts? I am afraid there aren't enough around.


*I copied this adjective from this great book. Unfortunately, I don't understand all of it. :(
I almost named my son "Leonard!"