Is the fastest route straight? │ The History of Mathematics with Luc de Brabandère
What is a cycloid curve?
And why is moving along it faster than travelling in a straight line?
Luc de Brabandère, in his series The History of Maths, explains how the cycloid curve has proved its value in the most everyday objects.
Find out more:
Travelling in a straight line is not the fastest route, not always. Try moving in a cycloid.
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Sometimes mathematics can help to correct our intuition. For example, I have a question for you: How many people do you need in a room to have a chance greater than 50% of having 2 people born on the same day? Maybe you'll think 100 people, or 50? No, 23 people are enough.
For example, if you take a soccer game. Twice 11 players + the referee, that makes 23. There is a probability greater than 50% that 2 people on the ground are born the same day. Mathematics can help a lot to deal with our intuition.
Another good example, but completely different - let's take 2 dots: A and B. You want a ball to go from A to B as fast as possible. Which path would you organise for the ball? The first intuition could be a straight line. Of course, it goes fast. But at the beginning it's a bit slow. So, you may have another idea, something like that: with a very strong start, because of the fall. Then you lose some momentum along the curve.
So, this is a simple question, but also a very tough question. Even Galileo was convinced that the fastest way for a ball to roll from A to B was a quarter of a circle. In fact, this is not the answer.
The real answer is what we call a cycloid. It's a very strange curve. The best way to draw and to understand what a cycloid is, is to take a table for example and a coin and let the coin roll along the table. Now take a fixed point on the coin, on the circumference, and follow the path of this fixed point. This curve is a cycloid. A cycloid is an example among many others of a fantastic formula, a fantastic curve. This curve, the cycloid, has many uses, and very strange properties.
For example: in clocks, before electricity of course, people had to use a pendulum to measure time. And you know what? If you take a pendulum and you jam the pendulum between 2 cycloids like this here, the amplitude has no impact, it will always be exactly the same time. It’s an ideal tool for manufacturing clocks. And on the top of that, you know what? The curve, the path followed by the pendulum here, is just another cycloid.
That's magic.
Leonhard Euler’s obsession with the bridges in his home city led to the birth of topology.
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