
Pythagorean Theorem and its many proofs - tomkwok
http://www.cut-the-knot.org/pythagoras/
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tokenadult
The Pythagorean Theorem is wonderful and very multicultural, as it is plain
that basic knowledge that the theorem applies to real-world measurement
problems is much earlier in time than the era of Pythagoras, and interesting
demonstrations of the theorem have arisen in several different parts of the
world. And the Cut the Knot site, from which this link is kindly submitted, is
a wonderful site about mathematics in general and should be known by all
readers of Hacker News.

Cut the Knot has another good page, "The Pythagorean Theorem is Equivalent to
the Parallel Postulate," pointing out that the conventional form of the
Pythagorean Theorem is a theorem only of Euclidean geometry, and the theorem's
statement has to be modified in non-Euclidean geometry. I make sure to tell
all my students that, even though my students are studying mathematics at the
"prealgebra" level and are of middle-elementary-school age (taking
supplementary classes for advanced learners). Learning non-Euclidean geometry
is harder if early math teachers don't mention that our usual school lessons
in geometry assume Euclidean geometry with the parallel postulate is the only
possible true description of the world. I like pointing my students to other
resources about non-Euclidean geometry and the parallel postulate for possible
optional further reading for them or for their parents.[2]

[1] [http://www.cut-the-
knot.org/triangle/pythpar/PTimpliesPP.sht...](http://www.cut-the-
knot.org/triangle/pythpar/PTimpliesPP.shtml)

[2]
[http://www.regentsprep.org/regents/math/geometry/gp13/Pythag...](http://www.regentsprep.org/regents/math/geometry/gp13/Pythag.htm)

[https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-
Euclid...](https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-
Euclidean_geometry)

[https://www.physicsforums.com/threads/what-happens-to-the-
py...](https://www.physicsforums.com/threads/what-happens-to-the-pythagorean-
theorem-in-a-non-euclidean-space.226522/)

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hyperion2010
Just to give an idea of how many proofs there are (and can be), I went to high
school with a girl who found a previously unpublished method of proving the
Pythagorean Theorem around 2002. I think we intuitively know that PT is a sort
of fundamental theorem for a huge number of different fields and the number of
proofs reflects the number of different areas that it constrains.

~~~
signa11
> I went to high school with a girl who found a previously unpublished method
> of proving the Pythagorean Theorem around 2002

if it is not too inconvenient, may you please link to it ? it would be
instructive to see a novel proof of something which has been around for
approx. 2500 years. thank you !

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jestinjoy1
There is even a proof by 20th United States President, James Garfield.
[http://jwilson.coe.uga.edu/emt668/emt668.student.folders/hea...](http://jwilson.coe.uga.edu/emt668/emt668.student.folders/headangela/essay1/pythagorean.html)

