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Math & Science

The Pythagorean Theorem

This morning I found the following at my place at the breakfast table. Kevin had finished an assignment early at school and the teacher said he could fill the remaining time by writing a paper on anything he wanted. This is what he did:
[Note that I've used "V" in place of the square root symbol, due to browser formatting limitations.]
-- Grantie, 3/30/2003

The Pythagorean Therom

The Pythagorean Therom

Before we talk much about the Pythagorean therom, there are three things you might not know about yet: Squaring, Variables, and Square roots.


You know multiplication (X), right? Well, squaring is when you multiply a number by itself. Here are a few examples.
2X2 =4 3²=9 4x = 16

You see I used three different ways to write squaring, #x#=#, #x=# and #²=X. So you know squaring now, right? 2²=4 3²=9 4²=16 5²=25 etc.

Variables (Algebra)

Variables are letters, or even abstract symbols used to stand for numbers, like say, a, b, c, m, n, r, x, & y. An equation with variables is called algebra. Heres an example: aX2 = 8. But you can also solve it: aX2 = 8 a = 4.

Algebra can be handy on some word problems.

Square Roots (V)

Square roots are the opposite of square numbers. Here's some examples. V4=2, V9=3, V16=4, V25=5 etc. Get it? O-kay. Now what we've all been waiting for.


The Pythagorean therom is a² + b² = c². Let's first say both a and b equal 1. 1² = 1, so a² + b² is equivalent to 1 + 1.

So if 1 +1 = 2, 2 = c²! So if c² = 2, c all by itself equals x2. But lets let c = x3. If we have b still equal one than what will a equal to still be a² + b² + c²? What squared + 1² will equal 3? Well, 2 + 1 = 3, so a² = 2, so a now = V2! So what if c² = 4? Well then a = V3! (3 + 1 = 4). So if c² = 5? Well then a = V4, which is the first (okay, 2nd) square root that's a whole number. c²=6, 9=V5. Can you figure out what a would equal if c=V7?

[answer: a=V6]

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