Spatial Reasoning and Mathematics
What happens when Pythagoras meets calculus? Mathematics elegantly combines abstract and spatial thinking.
There’s actually several different forms spatial reasoning takes in Mathematics. The first is in manipulation of notation, or ‘route-finding’ as I call it. The second is physical intuition in solving problems. These two are beautifully combined in finding the arc length of a curve, where we combine calculus and pythagoras.
Mathematics and Route-Finding
There’s a talent-delusion in mathematics.
We don’t say to someone: wow! you must naturally know your way around this local area. You were born with an understanding of the local geography! and then say to another person: unlucky: you were naturally born unable to find your way around town.
But this is what we do in mathematics. But here, the street signs and landmarks are theorems and notations. The local expertise and wisdom is the accumulated lemma and problems you’ve solved, and problems you’ve seen others solve. So when I say, get me from the bakers to the barbers, the novice wanders around in circles for hours, but you just need to line up a few dots (and then do the walking).
A large part of being good at mathematics — although there is talent involved — is like this. A mixture of…
