

Visual walk through of Euclid's proof of the Pythagorean theorem - vicapow
http://setosa.io/pythagorean/

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netrus
If you enjoy visualizations of Euclidean geometry, I highly recommend the work
of Byrne:

[http://www.math.ubc.ca/~cass/Euclid/byrne.html](http://www.math.ubc.ca/~cass/Euclid/byrne.html)

Example: [http://www.math.ubc.ca/~cass/Euclid/book1/images/bookI-
prop1...](http://www.math.ubc.ca/~cass/Euclid/book1/images/bookI-prop1.html)

(I found this to be one of the most impressive examples used by Edward Tufte
in his books).

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fuzionmonkey
Byrne's Elements is pretty remarkable. It's an interesting juxtaposition of
old 19th century typesetting (complete with initials) and comparatively
"modern" graphic design. Some pages look like they could be right out of De
Stijl.

Archive.org hosts a nice PDF copy, which I find more convenient than the
jpegs:
[https://archive.org/details/firstsixbooksofe00byrn](https://archive.org/details/firstsixbooksofe00byrn)

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onedognight
In case it's not obvious, you can drag the points in the diagram to change the
size of triangles and the associated squares.

~~~
clintonc
Also, if you hover over the geometric objects in the proof (like an AB or
ABC), the corresponding object is highlighted in the figure.

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justinpombrio
Or, if you want a proof with fewer words,
[http://isomorphismes.tumblr.com/image/790452593](http://isomorphismes.tumblr.com/image/790452593)

~~~
csense
This is probably the easiest, most intuitive proof of the Pythagorean Theorem.
Euclid's proof, by contrast, is a bit of a slog.

~~~
psykotic
Euclid has two proofs. The first is the one submitted here. The second one
uses the complicated theory of proportion from Book V. However, it's very
simple and intuitive when recast in modern terms. Take a right triangle ABC,
drop an altitude onto the hypotenuse, note the two smaller right triangles are
similar to ABC, calculate the area of ABC in two different ways using this
decomposition, and compare the results.

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symmetricsaurus
Very nice visualization.

Reading these old proofs is quite tedious but having this visualization makes
it much easier to follow.

Still, trying to understand Euclid makes you thankful for the more than 2000
years of advancements in mathematical notation and theory.

~~~
Jtsummers
> Still, trying to understand Euclid makes you thankful for the more than 2000
> years of advancements in mathematical notation and theory.

The importance of notation is greatly underestimated, IMO. Even when
programming, an arguably mathematical activity, many people still resist
improvements to notation that allow for clearer expressions. The contortions
some of my colleagues have gone through in Fortran or C++ (because they refuse
to use libraries that would clean up their code significantly, they roll their
own versions) to express their ideas.

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agumonkey
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.

[http://imgur.com/umPQpeu](http://imgur.com/umPQpeu)

ps: vector editor is not my website.

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Houshalter
I feel stupid. This is very difficult to follow.

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avmich
Not very clean. It's not immediately obvious how some statements are derived
from initial axioms.

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graeme
A bit OT, but I'm interesting in going through Euclid by drawing it with a
compass and ruler.

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.

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philtodd
I tried several times to explain the essence of Euclid's proof to a non-
mathematician (my wife). Here is the explanation which clicked.

[http://euclidsmuse.com/app?id=344](http://euclidsmuse.com/app?id=344)

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kljohnson
Here's another visual proof:

[http://mobius.maplesoft.com/maplenet/mobius/application.jsp?...](http://mobius.maplesoft.com/maplenet/mobius/application.jsp?appId=9468543)

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MarkTee
Here's a nice (physical) visualization that uses water:

[http://imgur.com/gallery/1ZGJGD6](http://imgur.com/gallery/1ZGJGD6)

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commlink
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.

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mannykannot
My thoughts exactly - then I found you can drag point C left and right.

Undocumented software!

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mishmax
Cool. What made you choose Angular over D3.js for this btw?

~~~
vicapow
It's using Angular with D3.

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gravity13
Interesting. What is Setosa?

