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Problem Solving Classroom

Tips from a Master Teacher (This is a work in progress.)

Snakes on a Plain

by Mark Illingworth
Snakes on a Plain

This is one of my favorite problems! I discovered it while flying back from Wichita where I had presented a workshop. I noticed the snaking rivers on the plains below and wondered about the mathematics. If I modeled the "snakes" with semicircles, would there be an ideal number of snakes that would make the river as short as possible. The results were more than cool, and I struggled with whether or not I should share my scribbles on cocktail napkins with the flight attendant.

Mathematics can be used to solve or model problems, but this set of challenges takes mathematics to a new level. It demonstrates how equations can be used as a language for understanding a phenomenon. This very important concept in science and engineering is often overlooked in math courses, so I hope that if nothing else you try this problem for yourself to see what I'm talking about.

Course(s): Geometry

Difficulty: 3/5

Length: long

Topics: circles, pi, circumference, literal equations

Problem Type: Problem Worth Solving

Layered by difficulty? yes

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