Posts Tagged ‘Fibonacci’

Happy Pi Day!

This Friday–March 14, is pi (pi) day.

Get it?  3-14.  3,141592 . . . . (the value of pi?)

The ultimate Pi Day was March 14 of 1592!  We gonna party like it’s 1592!

Maybe it’s a math geek thing.  Whoa!  Let’s not go putting labels on people here.

I was always intrigued by math in school, and math, be it algebra, trigonometry, geometry or calculus, was always one of my favorite subjects.

(pocket protector falls off and hits the floor.)

Okay.  I’m a math geek.

I was fascinated by numbers and how they related to the world around us.

The circumference of a circle is always 2 pir.  Why is that?  What is so special about  pi?  And is it not weird that the area of that circle is also related to this same, strange pi number, given that the area is equal to pi times the radius squared?  Every circle.  Everywhere.  Without exception.

It’s an irrational number.  It cannot be expressed as a fraction.  It is an endless series of non-repeating digits (the last report I saw was that it had been approximated to 12 trillion decimal places!)  According to Wikipedia (so it must be true!), “Attempts to memorize the value of π with increasing precision have led to records of over 67,000 digits.”  I have trouble remembering my Social Security number and my credit card number.  67,000 digits???  I would be terribly impressed if that wasn’t just so scarily inhuman.

piis also a transcendental number which means that it cannot be expressed as any combination of rational numbers, square roots or nth roots.  It also means that it is impossible to “square the circle.”  You cannot construct, using a straight edge and compass alone, a square whose area is equal to the area of a given circle.  Does that not just blow your mind???

piis also related to another irrational number (perhaps they are kissing cousins?) known as phi.  It is represented by another Greek letter: φ.  Obviously, they are both Greek.  Pi and Phi.  Sitting in a tree.  K-I-S-S-I-N-G.

φ is when the ratio of two numbers is equal to the ratio of the sum of those two numbers to the larger number, as described in this equation:  \frac{a+b}{a} = \frac{a}{b} \ \stackrel{\text{def}}{=}\ \varphi, and is referred to as the Golden Ratio.  \varphi = \frac{1+\sqrt{5}}{2} = 1.6180339887\ldots., another irrational number.

piis also related to the Fibonacci Series, which starts out 1,1,2,3,5 and continues with each succeeding number equal to the sum of the previous two numbers.  pi = 4*arctan(1/F(2n+2)) + 4*SUM{i=1...n}[arctan(1/F(2i+1))] where the Fibonacci Series is described by this: arctan(1/F(2i)) = arctan(1/F(2i+1)) + arctan(1/F(2i+2)).

I don’t know about you, but all this math is making me hungry.

I think I’ll go eat pie.

Happy pi Day!

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