Mechanical models that yield curious answers

Mechanical models that yield curious answers
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Everyone knows about the lever that could move the world. A lever is a mechanical tool that can multiply or divide an applied force over a distance and yield either a multiple of the distance or the force at the other end. The ratio is reasonably accurate, and, if the friction is actually negligible, it is possible to get a mathematically precise value for the ratio.

What other mechanical devices can be used to work out precise answers? There’s an example of a really complicated way to do something simple, using raindrops, here: https://www.reddit.com/r/dataisbeautiful/comments/84esm6/pi_as_calculated_by_raindrops_falling_on_square/ It works out the value of Pi, by counting the raindrops falling on a square plate and a round (circular) plate respectively. But is a powerful computer like an Arduino really needed for a simple counter?

So here’s the exercise: imagine that the same basic tools are used, a square plate and a circular plate. What simple mechanical counters can be attached to them, to count each raindrop that falls, and how can the counters be rigged to each other in order to yield a continuing calculation of the value of Pi, as the rain continues falling?

Can you build this model?

If you read the entire article, you’ll see that there are clues to working out the value of Pi even without counting each raindrop. So more models can be built that can deliver values for Pi.

Some interesting reading: look up the Difference Engine, or Analytical Engine. It was the first model of a general computing machine, 165 years ago. It was actually built, though at the time Charles Babbage thought of it, it was really difficult to make a machine accurately enough to work. It needed the soaring imagination of the brilliant Ada Lovelace, though, to work out how it would be programmed, so that it was much more than a mechanical calculator, it was a general purpose computer.

Today, the same kind of simple mechanical linkages that were available for them to use can be adapted to make a rainfall Pi calculator.

And, maybe, even adapted to yield other famous mathematical ratios.

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