Ask Uncle Colin: Are normals… normal? | Colin

Ask Uncle Colin is a chance to ask your burning, possibly embarrassing, maths questions — and to show off your skills at coming up with clever acronyms. Send your questions to and Uncle Colin will do what he can.

Dear Uncle Colin,

I don’t understand why the normal gradient is the negative reciprocal of the tangent gradient. What’s the logic there?

— Pythagoras Is Blinding You To What’s Obvious

Hi, PIBYTWO, and thanks for your message!

My favourite way to think about perpendicular gradients is to imagine a line going across a chessboard. Let’s say…

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