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The Calculus of a Shower That’s Either Too Hot or Too Cold

Finding the midpoint can be a struggle in higher mathematics, and in life.

9/27/2021 4:00:00 AM

Can’t get the shower faucet turned to just the right temperature? You’ve run afoul of the Intermediate Value Theorem, our columnist writes

Finding the midpoint can be a struggle in higher mathematics, and in life.

Mathematician Eugenia Cheng explores the uses of math beyond the classroom. Read more columnshere.I used a shower at the gym for the first time in a year and a half and couldn’t get it to the right temperature. First it was too cold, but if I turned the handle ever so slightly it immediately became too hot. I turned it the tiniest amount back, and it became too cold again. No position seemed to exist where it was at the right temperature for me, which means it violated a theorem from calculus called the Intermediate Value Theorem.

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