
Yes, this is the law.
The question is: WHY?
Could you show the WHY of this law in a short explanation?





I could, but these guys[^] have already done it for me.





Because multiplication is defined in such a way that that is true. Why does 1=1? Why does 1+1=2? You can only break down the math so far, eventually there is no reason other than the definition. See Godel's Incompleteness Theorems[^].





I wonder if there's a simple visual demonstration of why (for right triangles):
a^{2} + b^{2} = c^{2}






Nice!





Cool. Not as straightforward as the (a+b)^2 this though





There are many visual proofs to Pythagoras' theorem. For instance:
clicky for vimeo video[^]
Mind you, simply having the last frame of the video is probably enough for the visual proof.
Also, there is a whole wikipedia article on the subject of the Pythagoras' Theorem, and it includes some visual proofs, though I personally find the one in the video to be the most elegant.
Φευ! Εδόμεθα υπό ρηννοσχήμων λύκων!
(Alas! We're devoured by lambguised wolves!)





I like it.





Nice visual demonstration. I knew why but still amazing.
Also some other videos from him are cool!
All the best,
Dan





I never wondered why, actually. It was clear from the start.





good explanation...never saw that before.





I wonder if there's a simple visual demonstration of why every even integer greater than 2 can be expressed as the sum of two primes.





That would be a really awesome  that would mean Goldbach's conjecture is suddenly solved





Or even just a visual representation that makes primeness obvious.





Seems like there is such a way, but perhaps not for my brain. Ever read "The man who mistook his wife for a hat" by Oliver Sacks? In it, there are these two autistic twins who alternately recited 6 digit numbers to each other, then, as it dawned on the other that the number was prime, laughed out loud. The twins were separated by our friends at family services. Then there is that high functioning autistic guy "Daniel Tammet", who, in his book "Born on a blue day" tries to tell us about the topological landscape of numbers he sees and explores mentally. Fascinating stuff.





I doubt there is. If it was something that was easily recognizable, then it could be turned into an algorithm and there aren't any of those. The only things that I could think of would require an infinite dimensional drawing, so not very useful.
I haven't read either of those books, but they are now on my list.





I agree that it could be turned into an algorithm if we really knew what was going on. That's what makes it so intriguing to me .






much easier to disprove
smallest prime 2
so smallest sum of 2 primes = 2+2=4
3 is an integer > 2
3<4
by hypothesis 3 cannot be an integer > 2
contradiction therefore hypothesis is false





"even integer", not just "integer".





oops thats what I get for not reading it properly





Very nicely explained. I've never seen that before. Give that guy a medal!
His accent makes it all the more entertaining.
If your actions inspire others to dream more, learn more, do more and become more, you are a leader."  John Quincy Adams You must accept one of two basic premises: Either we are alone in the universe, or we are not alone in the universe. And either way, the implications are staggering”  Wernher von Braun





In South Africa we would say give that man a Bells(as in the whiskey)
But yeah that's very cool





I had a binomial cube[^] in my classroom when I was 4 years old.
There are a large number of objects like this that have been part of introducing mathematical concepts to young children as part of Montessori education for close to a hundred years now. Concepts are introduced using multiple senses: vision, touch, weight perception, hearing, etc. once the child becomes familiar with them in an intuitive sense, then the analytic concepts are introduced sometimes years later, but they are usually picked up pretty quickly because the groundwork has already been laid.



