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A comment on A visual proof that a^2 – b^2 = (a + b)(a – b). Parent comment

Re:A visual proof that a^2 – b^2 = (a + b)(a – b) by davrosthedalek on Sunday December 15, 2024 @04:25PM (#42426084)
That's the point. The geometric proof requires that you show the applicability for the b>a case with algebra. If you don't, it's not complete. And if you do, you can just show everything with algebra in the first place, and shorter, and also for a,b element C (instead of R), at the same time.
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Re:A visual proof that a^2 – b^2 = (a + b)(a – b) by TheRealPomax on Sunday December 15, 2024 @05:07PM (#42426315)
I'd have to disagree - it is perfectly fine to show a visual proof and simply state that we can reduce b>a to a>b and this proof therefore covers both, optionally with a little "I don't believe you, show me the math" pop out.

The visual proof is the neat part that people literally can't think of unless you show it to them, after which things might suddenly click for them. The algebraic proof is boring AF and doesn't make for a good maths hook ;)

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