Pythagoras and the Square !

Pythagoras is famous for his expertise with triangles. A famous and important mathematical formula learned in grade school is the Pythagoras' Formula.

"Pythagoras"

                                                     c² = a² + b<sup>2 

This formula is used to calculate the lengths of the sides of a special type of triangle called a "right" triangle.  To understand triangles, first we need to understand squares.</sup>  

If we read the formula aloud we would say,

" 'c' squared is equal to the sum of 'a' squared +' b' squared."

The letters a, b, and c  are used to represent numbers. That's ALGEBRA Baby!

For example:

5² = 3² + 4²

where c = 5, a = 3 and b = 4

The "superscript" '2' next to each number means "squared."

The official mathematical name for this superscript is "exponent." Exponents can be any number.

When a number has an exponent that is one of the counting numbers , i.e., an "integer", such as 1, 2, 3, 4, ... etc., it means that the the number (whose official mathematical name, by the way, is the "base") is to be multiplied by itself as many times as is the value of the exponent.

Example:      5² = 5 x 5

The base value 5 is multiplied by itself twice (it appears as a multiplier or "factor", twice.)

Another example : 6³ = 6 x 6 x 6  (6 is a factor 3 times)

Let's talk about the special case of  exponents of value  '2'.

Gee, Perfesser Wizard! Why is raising a base number to the exponent (or "the power of") 2 called "square"?

Think of a square.

A Square

It has a length and a width that are the same value. If we wish to know the area of the square (the part colored in red), then:

          area of square = length x width.

But because the length and width are the same size, we could say:

          area of square = length x length  

          which is the same as length²

or

         area of square = width x width

         which is the same as width²

So the word "square" is naturally associated with the exponent value 2.

Well then, what have we learned?

1.   The Pythagorean Formula
2.   Pythagoras was an expert on triangles. 
3.   Pythagoras knew a lot about squares too.
4.   What an exponent is.
5.   What a superscript is.
6.   What a base number is.
7.   How to calculate the area of a square.
8.   Why the exponent value 2 is called "the square."
9.   What an integer is.
10. What a  factor is.
11. Letters can be used to represent numbers in Algebra.
12. The length and width of a square are the same.

When you visit Perfesser Wizard, you don't go home empty handed!