[IAEP] [etoys-dev] TED - Alan Kay - Example(8:44)

[Edward Cherlin]

The book Pythagorean Proposition, by Elisha Scott Loomis, contains 367
proofs. Whatever floats your boat, say I. "You don't understand
anything until you learn it more than one way," says Marvin Minsky.

On Mon, Feb 22, 2010 at 05:21, Bert Freudenberg <bert at freudenbergs.de> wrote:
> On 22.02.2010, at 08:50, forster at ozonline.com.au wrote:
>>
>>> Here is an SVG of the simplest proof of the Pythagorean theorem I
>>> know, by dissection of a large square into five pieces that fit
>>> together into two smaller squares side by side.
>>
>> Thanks Edward
>>
>> I did not notice that no rotations were required (silly me)

I had hoped that coloring corresponding triangles would make that
obvious. However, as Prof. Shizuo Kakutani of Yale is quoted as
saying, "Sometimes we say that something is obvious, but it is not
obvious that it is obvious." ^_^

>> Implemented in Turtle Art, not so hard.
>> http://tonyforster.blogspot.com/2010/02/turtle-pythagoras.html
>
> That layout doesn't really convey the idea of the proof to me. This does:

In my diagrams, you move exactly two triangles from inside the first
square to get the second arrangement. The red line marks off the two
squares on the sides. Adding labels, or highlighting certain sides
further, should make the construction as obvious as you like.

Your version requires the preliminary step of proving (a+b)^2 = a^2 +
2ab +b^2 geometrically, or at least pointing out that your diagram
includes that proof. Caleb Gattegno has demonstrated that all of the
essential ideas of algebra can be taught in first grade, or even
kindergarten, using Cuisenaire rods, so this is not an obstacle.

> (from http://en.wikipedia.org/wiki/Mathematical_beauty)
>
> - Bert -
>
>
>
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-- 
Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin
Silent Thunder is my name, and Children are my nation.
The Cosmos is my dwelling place, the Truth my destination.
http://www.earthtreasury.org/