How To Memorize Pi

Pi is an irrational number. Allow to explain this to you:

A rational number is one that can be expressed as a ratio of two integers. Five is a rational number because it can be expressed as 5/1. Four-point-two is rational because it can be expressed as 42/10. Or 26/5. Or 462/110. Pi is an irrational number simply because it is not a rational number. There is no known way to express it as a ratio of two integers. Sure, we could try 314159265.../100000000... but we would never truly finish. The interesting thing is that we will never know for sure if pi is really irrational. It is so far, in what they've found (trillions of digits), but for all we know, it stops somewhere! Or it eventually goes into a never-ending repeating pattern. These are signs of rationality.

Other famous rational numbers include the square root of two, the square root of three, the square root of five, the square roots of lots of other numbers, the golden mean, e, and the reciprocals of all of these numbers.

Update: Hey! I just figured something out! If pi is simply a ratio of circumference and diameter, and pi is irrational and therefore cannot be expressed as a ratio of two integers, then the circumference and diameter of a circle can never both be integers! Yowza!

Did you know that figures as inaccurate as three have all been used for what we now call pi? The Old Testament itself gave that horribly off-key value, if I may. The Egyptians used 256/81, and the Babylonians used 3.125. The Hindus had a great start and used the value of approximately 3.1416 over 1500 years ago.

Thanks to Petr Beckman and his book, A History of Pi.

As if being this important circumference-diameter ratio isn't enough, pi can also be used to find the area of a circle! I will explain how. First, let us define the radius of a circle. The radius of a circle is a line segment extending from a point on the said circle to its center point. On the picture below, the radius would be a segment from the middle red point to any other red point, or anywhere on the green section for that matter.

Now that we have that settled, I'll assume that we all know how to raise to the second power, or to square a value. That's a value times itself. Okay. Now, here's the big formula: The area of a circle is equal to pi times the radius of that circle squared. In short,