Tag: geometry

Contributor Post Created with Sketch. Recommended by Ricochet Members Created with Sketch. Fun with Vectors and the Zombie Apocalypse

 

No, not vector in the epidemiological sense. The other, mathy kind of vector. Which, trust me, are fun. At least stick around for the zombies.

This dates back to my college days, when I took Differential Equations. Twice. I’ve always been good with math. Sure, I struggled with plenty of things along the way (percentages, trig identities, multivariable integration. Oooh, and concentrations in chemistry), but DiffEq is where I hit the wall like a coyote hits his own painted-on tunnel. Vector spaces were part of that; an abtruse concept used to justify an abstract concept used to solve some difficult equations that might, in turn, have something to do with the real world. But once I got my head wrapped around them, vector spaces turned out to be a fun and useful bit of math. Hey, it could happen.

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Contributor Post Created with Sketch. Recommended by Ricochet Members Created with Sketch. Kitchen Math: Building the Primordial Pyramid from Cheese Singles

 

Those of you who remember the formula for the volume of a pyramid and its rounder cousin the cone may have, like me, have been told to simply accept it, at least until we learned calculus – that is, if we learned calculus. When I was in school, this bugged me. Bugged me enough to doodle a lot of pyramids until I discovered the primordial pyramid. The primordial pyramid is the only pyramid I know of which makes its volume obvious without the use of calculus – heck, nearly without the use of math! It is, however, a pyramid with specific proportions, incapable of answering for all pyramids and cones. To make it do that takes magical cheese.

Imagine a perfect cube. It could be a perfect cube of cheese, but at this point it’s more helpful to picture the cube as transparent – made of jello, for example. Picture lines inside the cube connecting each corner of the cube to its most opposite corner. The surfaces connecting these lines divide the cube up into six identical pyramids, primordial pyramids. The height H of each primordial pyramid is one-half the height of the cube, so the volume of the cube is (2H)^3. Because six of these pyramids together form the cube, the volume of each pyramid is (2H)^3/6. The base of each pyramid has area A = (2H)^2. Writing the volume of the primordial pyramid in terms of base and height, the volume is 2HA/6 = 1/3 HA. Now suppose we build a primordial pyramid out of that American kitchen staple, cheese singles (very thin, identical squares of cheese food product):

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