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Hatesmondays
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What are some cool things that people can do with the Pythagorean Theorem?
Here are 109 other proofs: http://www.cut-the-knot.org/pythagoras/Hatesmondays said: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"
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".)Enigman said: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.
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.Hatesmondays said:What are some cool things that people can do with the Pythagorean Theorem?
Hatesmondays said:What are some cool things that people can do with the Pythagorean Theorem?
I like that one.Hornbein said: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.
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).
Ooh ooh, I remember this from physics! We used an inductor to improve efficiency! (decrease the non-doing reactive power)berkeman said: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 [Broken]
http://www.rbgrant.co.uk/wp-content/uploads/2012/11/Power-Factor-Correction-2.jpg [Broken]
Borek said:Prove it.
Hatesmondays said:That is right! I'm am going to try to disprove it. On another site cuase this one doesn't allow new ideas.
Let [itex]1\in\mathbb{Z}_2[/itex], then [itex]1+1 = 0[/itex] :D :Dmicromass said:- Disprove that 1+1=2
nuuskur said:Let [itex]1\in\mathbb{Z}_2[/itex], then [itex]1+1 = 0[/itex] :D :D
It is very easy to disprove the pythagorean theorem! First, bring a ball ...micromass said:If you enjoy to disprove stuff that is true, I can give you some other suggestions:
...
micromass said:- Disprove you exist
Hatesmondays said:I exist?
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 said:Boom there.
collinsmark said: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
Hatesmondays said:I exist?
micromass said:I didn't ask to prove you exist, I asked to disprove you exist.
The Pythagorean Theorem can be used to find the distance between two points on a coordinate plane by using the formula c = √(a^2 + b^2), where c represents the distance between the two points and a and b represent the lengths of the sides of a right triangle formed by the two points.
Yes, the Pythagorean Theorem can be used to solve real-life problems such as finding the length of a ladder needed to reach a certain height on a wall or the distance a person needs to travel to get from one point to another. It is a useful tool in fields such as architecture, engineering, and navigation.
The Pythagorean Theorem can be used to find the length of a diagonal in a rectangle by using the formula c = √(a^2 + b^2), where c represents the length of the diagonal and a and b represent the lengths of the sides of the rectangle. This is because the diagonal of a rectangle forms the hypotenuse of a right triangle with the sides being the length and width of the rectangle.
Yes, the Pythagorean Theorem can only be applied to right triangles, which are triangles with one angle measuring 90 degrees. This is because the theorem is based on the relationship between the sides of a right triangle and the length of its hypotenuse.
Yes, the Pythagorean Theorem has many applications in other areas of mathematics such as trigonometry, geometry, and algebra. It is also a fundamental concept in the study of the Pythagorean triples, which are sets of three positive integers that satisfy the theorem.