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never heard of them being called legs
adamennis999 1 year ago
This has been flagged as spam show
Let n be any integer gretaer or equal to 3, then:
1- for any polygon with sides x1, x2, ..., xn-1 and xn, if that polygon has a longest side, say xn, then x1^r + x2^r + ... + xn-1^r = xn^r, where r is some real number greater than 1.
2- In the following equation:
x1^r + x2^r + ... + xn-1^r = xn^r, if r is any real number greater than 1, then x1, x2, ..., xn-1 and xn must be the lengths of the sides of some n-sided polygon.
jahdallah 3 years ago
In 4:50 how about justifying the 90 deg. by a symmetry argument using a 90dg. rotation on the square? I'd use either argument, but this one probably works better for eager students.
jupiterjjrm 3 years ago
There are lots of ways to skin this cat.
Actually, if you're teaching, it's a good idea to show more than one proof of this theorem, just to show that while there's only one answer to the problem (in that, the pythagorean theorem is true), there are lots of ways to get to that answer.
meepsmathmatters 3 years ago
Oh, what a beautiful proof. But, excuse me what Q.E.D. does mean? Thank you very much.
geomong 4 years ago
Q.E.D. literally means "quod erat demonstrandum", Latin for (roughly) "I have demonstrated that", meaning "the proof is finished".
It's a common way to indicate the end of a mathematical proof.
meepsmathmatters 4 years ago
I have lost count of the number of coffee+Bailey's I've earnt during my teens with this proof and some triangular number tricks! ;D Who would have thought this kind of stuff would be so useful in bars with people who have long hated maths?! I swear it works! It can even be sexy!
jupiterjjrm 3 years ago
Yay for Irish coffee!
meepsmathmatters 3 years ago
LOL
jupiterjjrm 3 years ago