Assuming √2 is rational, √2=a/b where a and b are integers and the fraction is in the lowest terms. Then a²=2b², so there are 2 squares with integer sides such thatpic.twitter.com/pnVJis2Cqp
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Assuming √2 is rational, √2=a/b where a and b are integers and the fraction is in the lowest terms. Then a²=2b², so there are 2 squares with integer sides such thatpic.twitter.com/pnVJis2Cqp
Placing the 2 smaller squares on the larger one, we see that the sum of the areas of the corner squares must equal the area of the black central one. We reached a contradiction since we assumed a and b are the smallest integers such that a²=2b²!pic.twitter.com/2xMt3MN2zL
√2 is irrational Proof. If √2=a/b (in reduced form with integers a,b), then a²=2b². Since odd×odd=odd and a² is even, a must also be even, but then a² is divisible by 4, so b²=a²/2 is even implying that b is also even. This is a contradiction. QED
I liked to show this #proofinatweet mod 3 to my students.
RIP Alex. @CutTheKnotMathhttps://twitter.com/CutTheKnotMath/status/203147607856525312?s=19 …
This visually explains the comcept of surds....
well explained @fermatslibrary
Can you explain why a2=2b2? Sorry, it seems obvious to you all ..
I can even extend it to saying that: none of the roots of 2 is rational! Proof:pic.twitter.com/JqS3D0lkim
Proof by contradiction..
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