What are some cool things that people can do with the Pythagorean Theorem?
A discussion of the Pythagorean Theorem with various proofs:
EDITTED by mentor to remove the duplicate content and leave the URL for reference.
The last time I used it was to find the "normal lens" for my cameras.
Here's the wiki article:
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.
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.
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".)
I used it (iteratively) to generate π once.
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.
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.
A Mathematical Fable
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:
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...
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.
Ooh ooh, I remember this from physics! We used an inductor to improve efficiency! (decrease the non-doing reactive power)
You can effectively proof the time dilation formula from Special Relativity using little more than Pythagoras. That might be considered cool.
It's even cooler to disprove it!
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
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