Tag: Math

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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I went to pick up a take-out order from a restaurant today and found a dozen or so customers sitting around with no food. The restaurant’s computer system was down.  In the old days, we could calculate totals manually and even take credit card payments via a non-electronic system. But the young clerk just kept […]

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The Night of Fire

 

Blaise Pascal, mathematician, scientist, inventor, and philosopher, a man who from the age of 16 had been making historic contributions to mathematics and the physical sciences, who, despite a sickly constitution and a capacity for intense abstraction nonetheless oversaw the material construction of his experiments and inventions with great zest, was barely past 30 when saw something unexpected one raw November night. He saw fire. The vision of it so branded him that he sewed the record he made of it, his Memorial, into his coat, carrying it with him the rest of his life:

Memorial, Pascal

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What strange things do you do that you worry might get reported as terrorist activity? For many years, my greatest fear was my metronome, which I had reason to carry around with me wherever I went, including on plane flights. I mostly used it for its tuner function, but it wasn’t hard to accidentally press […]

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I have little doubt that Zipf’s Law is not new to a great many Ricochetois, considering how many of y’all have brains the size of planets, but it was a new concept for me when I clicked on this highly fascinating YouTube video from VSauce: Preview Open

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You have a box of 1500 screws. They’re inventory, they cost about a dollar each, and you want to send them out with your guys on various jobs over the next nine months or so. To track them, you want to parcel them out into bags, each of which contains 100 screws. You have a […]

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I was trying to remember how to do it last night at work, and it remains elusive. I work support in a Hard Drive parts factory. We audit our manufacturing lots regularly through the process for defects. Last night I was tasked with tracking down an elusive problem. In a particular audit we inspect 54 […]

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