If you enjoy visualizations of Euclidean geometry, I highly recommend the work of Byrne:<p><a href="http://www.math.ubc.ca/~cass/Euclid/byrne.html" rel="nofollow">http://www.math.ubc.ca/~cass/Euclid/byrne.html</a><p>Example: <a href="http://www.math.ubc.ca/~cass/Euclid/book1/images/bookI-prop1.html" rel="nofollow">http://www.math.ubc.ca/~cass/Euclid/book1/images/bookI-prop1...</a><p>(I found this to be one of the most impressive examples used by Edward Tufte in his books).
Or, if you want a proof with fewer words,
<a href="http://isomorphismes.tumblr.com/image/790452593" rel="nofollow">http://isomorphismes.tumblr.com/image/790452593</a>
Very nice visualization.<p>Reading these old proofs is quite tedious but having this visualization makes it much easier to follow.<p>Still, trying to understand Euclid makes you thankful for the more than 2000 years of advancements in mathematical notation and theory.
Funny, few days ago I wanted to write it from scratch starting through the geometric 'interpretation', just to see if I remembered. I had to use `square of sum` identity though.<p><a href="http://imgur.com/umPQpeu" rel="nofollow">http://imgur.com/umPQpeu</a><p>ps: vector editor is not my website.
A bit OT, but I'm interesting in going through Euclid by drawing it with a compass and ruler.<p>Is there any good guide to doing this? I have Byrne's copy of Euclid. But I found there were multiple points I got stuck when trying to draw it myself.
I tried several times to explain the essence of Euclid's proof to a non-mathematician (my wife). Here is the explanation which clicked.<p><a href="http://euclidsmuse.com/app?id=344" rel="nofollow">http://euclidsmuse.com/app?id=344</a>
Here's a nice (physical) visualization that uses water:<p><a href="http://imgur.com/gallery/1ZGJGD6" rel="nofollow">http://imgur.com/gallery/1ZGJGD6</a>
Well done, but it would have been better if the graphics depicted a right scalene triangle -- the more general case -- rather than a right isosceles triangle.