

Surprising Uses of the Pythagorean Theorem - brett
http://betterexplained.com/articles/surprising-uses-of-the-pythagorean-theorem/

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mrtron
I really like the concept surrounding sorting.

It really helps you visualize why you need to separate your lists into smaller
piles before sorting if you can, since it takes the same amount of time to
sort a 50 element list as it does sorting a 40 and a 30 both.

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pixcavator
"Throughout our school life we think the Pythagorean Theorem is about
triangles and geometry." Some of us still do. What he is talking about is
Pythagorean triples. Well, maybe. Energy, for example, does not have to be an
integer, so it's not really about Pythagorean triples. What is the point?

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kalid
Hi, you don't have to split a triangle into integers. For example, you could
have

50^2 = 25^2 + 43.3^2

Strictly speaking, if you have a circle of radius 50, you can take the sine
and cosine of any angle and get a possible way to split the length.

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pixcavator
Fair enough. Still, what is the point of the article? Some additive quantities
are squares of other quantities, you add them, and it looks like the
Pythagorean Theorem, without triangles... Is that it?

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kalid
Two main points, mostly to look at this old theorem in new ways.

1) The sides of a triangle (3-4-5) can represent portions of _any_ shape. For
example, circle area (radius 3) + circle area (radius 4) = circle area (radius
5).

Instead of radius, you could pick diameter, circumference, or any line segment
and the relationship would hold.

2) You can use the Pythagorean Theorem to split any squared quantity into two
smaller ones. This can yield surprising insights; is it immediately clear that
a list of 50 takes as long to bubble sort as a list of 30 and 40? =)

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pixcavator
There may be a point here, but I am still uncomfortable with the use of the
Pythagorean theorem here. Even if applied to areas only, it seems like a
stretch. In fact with this approach one can suggest other identities. For
example, if you replace squares with cubes (or circles with spheres), you will
have a^3+b^3=c^3. And this clearly has nothing to do with the Pythagorean
theorem.

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testapplication
You might want to try that math again; it doesn't work for spheres.

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pixcavator
What math?

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jgamman
this is why i surf hacker news...

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injesus
I'm not sure if this was an add, but I got a virus hit from this site.

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injesus
Trying to warn people that an advert is showing up as a virus when you click
on the link to this site. How that is worth negitive points I don't know?

