The two rectangles are congruent. What’s the shaded area?pic.twitter.com/didtAhl6tG
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Mathematical physicist and mentor to mathematically talented youth. Talent is that which bridges the gap between what can be taught and what must be learned.
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The two rectangles are congruent. What’s the shaded area?pic.twitter.com/didtAhl6tG
Actually, it's much simpler:pic.twitter.com/2AP43NvCK2
Thanks! It's funny how important simplifications are found the second time you look at a solved problem ...
I think knowing the answer already is key to this. I often look at a problem with a nice answer coming out of a roundabout method and think “surely that’s not a coincidence”... and then (with any luck) I realise there’s a nice method I could have used all along.
This is indeed mostly how things proceed, and one should never feel the slightest shame in using even the most repulsive and unnatural methods to arrive at a correct answer, especially at first. But it's almost always possible to do better -- and one should always aspire to.
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