Pythagorean Theorem
Friday, January 09, 2009
What is Pythagorean Theorem aka Theorem Pythagoras? This may be ask by some people out there? Well, the theorem is as below:
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
and it usually summarized as follows:
The square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides.
Let me simplify in a simplest formula:
Sounds familiar for some readers out there? Yes! We'd learn it in high school years where we're given formulas to find the length of the right angle triangle. Now, we just only need to memorise the formula and just applied it. And we're actually forgotten the most important part:
How they find the formula out? How can they proof it? Why they can produce such formula?
We're taking things for granted and sometimes we're actually forgot to appreciate it.
Okay. My main point for this post is to show something very interesting. They're actually many ways to proof this theorem, such as using similar triangles, Euclid's proof, Garfield's proof, Similarity proof, Algebraic proof, Proof by differential equations and Proof by rearrangement.
Today I'll show you how to proof this theorem by using rearrangement proving. This is also just one example among all kinds of arragement proving. It's very easy. Even elementary students can proof it!! ^^
First, measure and draw a some sort of combination of 2 squares like above
Then, cut of the shaded area... 
And connect it to the other edge... And you'll find it is actually another bigger square!!
So, what's the connection some may ask?
During the measurement, it is actually a 2 square that I'd just mentioned, where the smaller square's area is 3square whereas the bigger ones is 4 square...
.. and the cut and paste resulting square with it's area of 5 square~ And this leads to...
.. the Pythagorean Theorem!!! Easy eh? So, what do you think? A very simple thing that sometimes we won't realise but it's actually may lead to some new thing. Interesting eh?
From this simple thing, more people will able to understand to proof the theorem and parents even can teach this theorem by introducing it as a 'game'!!! ^^
Posts
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