Cool ways to use the Pythagorean Theorem

[Hatesmondays]

What are some cool things that people can do with the Pythagorean Theorem?

 

[Borek]

Prove it.

 

[Hatesmondays]

Prove what?

 

[Borek]

The theorem.

 

[Hatesmondays]

A discussion of the Pythagorean Theorem with various proofs:

http://jwilson.coe.uga.edu/emt668/emt668.student.folders/headangela/essay1/pythagorean.html

EDITTED by mentor to remove the duplicate content and leave the URL for reference.

 

[zoobyshoe]

The last time I used it was to find the "normal lens" for my cameras.

Here's the wiki article:

http://en.wikipedia.org/wiki/Normal_lens

Basically, the "normal" lens for any given camera is that lens which is middle of the road, being neither wide angle nor telephoto. What focal length that is for any given camera is dictated by the film or sensor size. It is that focal length which is equal to the length of the diagonal of the format or sensor. Knowing the sensor width and height, it is a simple matter to use Pythagorean theorem to find the diagonal.

 

[Enigman]

Pythagorean Theorem
The theorem states that:

"The square on the hypotenuse of a right triangle is equal to the sum of the squares on the two legs"

Here are 109 other proofs: http://www.cut-the-knot.org/pythagoras/
There are at least 370 of them, according to wiki. Including one by U.S. President James Garfield.
Hence, finding new proofs are a cool thing to do. Q.E.D.

 

[S.G. Janssens]

There are at least 370 of them, according to wiki. Including one by U.S. President James Garfield.
Hence, finding new proofs are a cool thing to do. Q.E.D.

Would it be possible, using certain foundational results in mathematics or logic that I am shamefully unaware of, to establish an upper bound on the number of different proofs? (For this one of course first has to specify when two proofs are considered "different".)

 

[tfr000]

I used it (iteratively) to generate π once.

 

[Hornbein]

What are some cool things that people can do with the Pythagorean Theorem?

The sum of the squares of the standard deviations of two independent random variable is equal to the square of the standard deviation of their sum.

 

[Hornbein]

What are some cool things that people can do with the Pythagorean Theorem?

I like that works with any number of dimensions. a^2 + b^2 + c^2 + ... + y^2 = z^2

It is even used in infinite dimensions, with the proviso that the sum has to be finite.

 

[Hatesmondays]

I like that works with any number of dimensions. a^2 + b^2 + c^2 + ... + y^2 = z^2

It is even used in infinite dimensions, with the proviso that the sum has to be finite.

I like that one.

 

[collinsmark]

A Mathematical Fable

 

[berkeman]

I've been working with Power Factor a lot lately in my EE work. The Pythagorean Theorem comes up in the vector addition of Real and Reactive Power:

http://www.rbgrant.co.uk/wp-content/uploads/2012/11/Power-Factor-Correction-2.jpg
http://www.rbgrant.co.uk/wp-content/uploads/2012/11/Power-Factor-Correction-2.jpg

http://www.rapidtables.com/electric/electric_power.htm

Real / reactive / apparent powers relation
The real power P and reactive power Q give together the apparent power S:

P^2 + Q^2 = S^2

P is the real power in watts [W]

Q is the reactive power in volt-ampere-reactive [VAR]

S is the apparent power in Volt-amper [VA]

Power factor definition
The power factor is equal to the real or true power P in watts (W) divided by the apparent power |S| in volt-ampere (VA):

PF = P(W)/ |S(VA)|

PF - power factor.

P - real power in watts (W).

|S| - apparent power - the magnitude of the complex power in volt·amps (VA).

A power factor of 1.0 is ideal, and devices with input Power Factors < 1.0 are starting to have to use "Power Factor Correction" to bring up their low numbers...

 

[2milehi]

Tiling a floor - Measure one side (A) at 10 feet and mark both ends, at one of the ends of A make a perpendicular arc 10 feet long. On the other end of A, measure 14.14 feet and scribe an arc to intersect with the first arc.

 

[nuuskur]

I've been working with Power Factor a lot lately in my EE work. The Pythagorean Theorem comes up in the vector addition of Real and Reactive Power:

http://www.rbgrant.co.uk/wp-content/uploads/2012/11/Power-Factor-Correction-2.jpg
http://www.rbgrant.co.uk/wp-content/uploads/2012/11/Power-Factor-Correction-2.jpg

Ooh ooh, I remember this from physics! We used an inductor to improve efficiency! (decrease the non-doing reactive power)

 

[PeroK]

You can effectively proof the time dilation formula from Special Relativity using little more than Pythagoras. That might be considered cool.

 

[PeroK]

Prove it.

It's even cooler to disprove it!

 

[Hatesmondays]

That is right! I'm am going to try to disprove it. On another site cuase this one doesn't allow new ideas.

 

[micromass]

That is right! I'm am going to try to disprove it. On another site cuase this one doesn't allow new ideas.

If you enjoy to disprove stuff that is true, I can give you some other suggestions:
- Disprove the theory of evolution (this is a popular one, googling will get you a lot of references!)
- Disprove germ theory
- Disprove gravity
- Disprove that Earth is round
- Disprove that 1+1=2
- Disprove you exist

 

[nuuskur]

- Disprove that 1+1=2

Let 1\in\mathbb{Z}_2, then 1+1 = 0 :D :D

 

[micromass]

Let 1\in\mathbb{Z}_2, then 1+1 = 0 :D :D

Not a disproof since 0=2 in $\mathbb{Z}_2$.

 

[nuuskur]

Unfortunately true, but worth a shot.

 

[Intrastellar]

If you enjoy to disprove stuff that is true, I can give you some other suggestions:
...

It is very easy to disprove the pythagorean theorem! First, bring a ball ...
Not going to finish the proof to avoid spoilers

Edit:
Although I suppose that an assumption of the theorem is that you are not allowed to bring a ball

 

[Hatesmondays]

- Disprove you exist

I exist?

 

[Hatesmondays]

Boom there.

 

[collinsmark]

I exist?

Boom there.

The fact that' you're even able to even ask that question proves [to you] that you exist. (Proves it to yourself, that is. It doesn't necessarily prove it to anybody else; that's a significantly more difficult problem. But if you're capable of asking yourself about your own existence, it proves to yourself that you exist. https://en.wikipedia.org/wiki/Cogito_ergo_sum.)

 

[Hatesmondays]

The fact that' you're even able to even ask that question proves [to you] that you exist. https://en.wikipedia.org/wiki/Cogito_ergo_sum

Crud.

 

[micromass]

I exist?

I didn't ask to prove you exist, I asked to disprove you exist.

 

[Hornbein]

I didn't ask to prove you exist, I asked to disprove you exist.

I don't think, therefore I am not.

 

[Hatesmondays]

Well...