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A comment on Monumental advance in number theory posted to the ArXiv by Yitang Zhang. Parent comment

Re:Monumental advance in number theory posted to the ArXiv b... by robertlagrant on Tuesday November 08, 2022 @05:23AM (#33517753)
When I came across the (obvious, in retrospect) visual explanation for why (a + b)(a + b) == a^2 + 2ab + b^2 I was blown away by how simple it was, and by why on earth I had to just memorise that formula in school.
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Re:Monumental advance in number theory posted to the ArXiv b... by germandiago on Tuesday November 08, 2022 @05:32AM (#33517807)
This is exactly the kind of intuitions I am talking about. Much easier to explain like that.
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Re:Monumental advance in number theory posted to the ArXiv b... by n4r9 on Tuesday November 08, 2022 @10:21AM (#33519936)
By "visual explanation" do you mean imagining a square whose sides are length (a + b), and breaking it up into smaller squares and rectangles?

Or do you mean mulitplying out the terms:

  (a + b)(a + b) = a^2 + ab + ba + b^2 = a^2 + 2ab + b^2

?
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Re:Monumental advance in number theory posted to the ArXiv b... by robertlagrant on Tuesday November 08, 2022 @10:25AM (#33519986)
The former, yes.
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Re:Monumental advance in number theory posted to the ArXiv b... by n4r9 on Wednesday November 09, 2022 @09:59AM (#33532484)
It's interesting that some people find that way easier to remember. For me, multiplying out the terms seems faster, probably only because I've practised so many times in my life that I can picture the algebra in my head. It also seems more general, as it's a technique which you have to know anyway. I guess it comes down to being more geometrically minded vs algebraically minded. School should try to cater to both!
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Re:Monumental advance in number theory posted to the ArXiv b... by robertlagrant on Thursday November 10, 2022 @03:20PM (#33552672)
I wouldn't use it to calculate, but I would use it to explain why the calculation is what it is.
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