# Cool ways to use the Pythagorean Theorem

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1. Oct 26, 2015

### Hatesmondays

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

2. Oct 26, 2015

### Staff: Mentor

Prove it.

3. Oct 26, 2015

### Hatesmondays

Prove what?

4. Oct 26, 2015

### Staff: Mentor

The theorem.

5. Oct 26, 2015

### Hatesmondays

Last edited by a moderator: Oct 27, 2015
6. Oct 26, 2015

### 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.

7. Oct 27, 2015

### Enigman

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.

8. Oct 27, 2015

### Krylov

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".)

9. Oct 27, 2015

### tfr000

I used it (iteratively) to generate π once.

10. Oct 27, 2015

### Hornbein

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.

11. Oct 28, 2015

### Hornbein

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.

12. Oct 28, 2015

### Hatesmondays

I like that one.

13. Oct 28, 2015

### collinsmark

A Mathematical Fable

14. Oct 30, 2015

### Staff: Mentor

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.rapidtables.com/electric/electric_power.htm
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...

Last edited by a moderator: May 7, 2017
15. Nov 1, 2015

### 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.

16. Nov 3, 2015

### nuuskur

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

Last edited by a moderator: May 7, 2017
17. Nov 3, 2015

### PeroK

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

18. Nov 3, 2015

### PeroK

It's even cooler to disprove it!

19. Nov 6, 2015

### Hatesmondays

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

20. Nov 7, 2015

### micromass

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

21. Nov 7, 2015

### nuuskur

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

22. Nov 7, 2015

### micromass

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

23. Nov 7, 2015

### nuuskur

Unfortunately true, but worth a shot.

24. Nov 7, 2015

### Intrastellar

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

25. Nov 7, 2015

I exist?