Rubber band “Slide Rule” does not slide, but rotates

Here we especially enjoy slide rules. We even have our own collections, including some cylindrical and round collections. But [Mathologer] discusses a recent Reddit post explaining a circular slide rule-style device using a wheel and a stretchy rubber band. While it would probably be difficult to build the actual device with a rubber band, it can do wonders for your understanding of logarithms that still appear in our lives when you calculate decibels, for example. [Dimitri] simulated the rubber band for you in software.

The idea is that on a perfect rubber band, numbers from 0 to 10 are evenly marked. If you spin a wheel attached to the 10th mark, the rubber band will stretch more and more. So the 10 and the 9 have relatively little space between them, but the 1 and the 2 are much further apart. The circumference of the wheel is set so that the 1 will lie exactly over the 10. This means that any spot on the wheel can represent any number that differs by only one decimal. So you could have 3, mean 0.03, 300, or — of course — 3. Of course you don’t have to build the wheel with a rubber tire – you can just mark the wheel as a regular circular slide rule.

If you’ve never really learned why a slide rule works or don’t know how to use one, you’ll find the explanations in the video very intuitive and enlightening. You should have a rough idea of ​​the magnitude of the answer you expect, but with practice it’s not that difficult.

If you flatten the circle, you will of course get a regular slide rule. You can see some of my collection — but oddly none of my round — in an old post from 2015. If you’d like to make your own, we suggest you leave the rubber band in the drawer and checkout. [Dylan’s] work.

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