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Visualizing mathematics

| Posted on: August 27th, 2008 | Categories: Creativity, Design, Fun, Good | Bad Design, Mathematics, Representation, Teaching, Technology, Uncategorized, Worth Reading | 1 Comment »
Other related posts and pages: |By the Numbers | Exploring visual space with mathematics | Ideas are cool | Word cloud | Gallimaufry |

I love visual proofs of mathematical theorems. One visual proof I use quite often in my design courses (CEP817 or CEP917) is a visual proof of the fact that the sum of consecutive odd numbers is a square number.

In other words:

1 + 3 = 4 = 22

1 + 3 + 5 = 9 = 32

1 + 3 + 5 + 7 = 16 = 42

… and so on.

Mathematically speaking that translates to

1 + 3 + … + (2N-1) = N2

Now one can go about proving this fact this through algebra OR one could just do it visually. Check out this image below,

… or better still go to this applet

Pretty cool huh?

Looking for the above applet led me to this other cool visual proof for

(a + 1)2 = a2 + 2a + 1

Check it out.


| Posted on: August 27th, 2008
Other related posts and pages: |By the Numbers | Exploring visual space with mathematics | Ideas are cool | Word cloud | Gallimaufry |


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One Response to “Visualizing mathematics”

  1. leigh Says:
    August 27th, 2008 at 11:58 am

    Triggered me to remember these visual thinking videos from kermit:
    original – http://www.youtube.com/watch?v=pU57i9rxoYU
    remake – http://www.youtube.com/watch?v=fcqY66chhCA

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