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.

-Source from Wikipedia-

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'!!! ^^

6 comments: to “ Pythagorean Theorem

  • Lee Yee
    Friday, January 09, 2009 10:28:00 AM  

    cham... someone zhou huo ru mo...

  • xinying
    Friday, January 09, 2009 6:35:00 PM  

    is not zhou huo ru muo lar... just interesting...

  • Anonymous
    Sunday, August 29, 2010 8:45:00 PM  

    Awesome site, I hadn't noticed before during my searches!
    Continue the good work!

  • Anonymous
    Friday, September 17, 2010 7:05:00 AM  

    Wow neat! This is a really great site! I am wondering if anyone else has come across something
    like this in the past? Keep up the great work!

  • Anonymous
    Monday, January 28, 2013 12:19:00 AM  

    Hello. Facebook takes a [url=]craps[/url] wager move in reverse on 888 casino see trade: Facebook is expanding its efforts to make something speed up real-money gaming to millions of British users after announcing a grab with with the online gambling comrades 888 Holdings.And Bye.

  • Anonymous
    Monday, April 29, 2013 3:12:00 AM  

    A great pair of trainers, perhaps not the foremost gorgeous, not the more expensive, neither is business name, but it surely may take you to definitely tour the globe, Christian Louboutin Sale
    resolve experience the happiness shoes it's best not to fit, perhaps enviable,nevertheless, the injured indeed.
    A great situation you'll want to have encountered, walked vertical watching the display cabinets in countless types of shoes you come across dazzling, absolutely no way of choice. Its cost is in line is not actually beautiful, like very costly, comfortable transparent fashion, feel good-looking men and women that think old-fashioned ... turn into completely pleased about simply difficult. Pick to settle on, finally decided on a pair, wear a while only to discover foot wear, or possibility to accommodate their clothes,Christian Louboutin Sale
    simple methods to make this happen time? Giving up'd rather painful to need to wear?

Post a Comment