What’s so difficult about Pi? │ The History of Mathematics with Luc de Brabandère
The constant Pi is one of the world’s oldest enigmas.
Extremely difficult to define exactly, its trillion-digit decimal sequence has confounded mathematicians for centuries.
Philosopher Luc de Branbandère guides us through the history of mathematics, from Egyptians measuring with the Sun to modern algorithms for self-driving cars.
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The constant Pi is one of the oldest enigmas in maths. They even named a day after it. Subscribe now to the series ‘The History of Maths’ on the YouTube channel ‘What makes it tick?’
In the country of mathematics, there are some famous numbers. We've already met the golden number. We've already met E and of course the ultimate Pi. Pi is strange because it's very easy to define, very difficult to calculate. And more than that, Pi is a mystery.
The definition is simple. You take a circle and the diameter. Pi is the ratio between the length of the circle and the straight line. Roughly equal to 3.14. It looks simple; it's an incredible mystery, we don't even understand the sequence of the decimals.
One of the oldest problems in mathematics was called ‘squaring the circle.’ That was a challenge for mathematicians a long time ago, and still today. It was just to build the square the same surface as a given circle. Nobody can solve this, now we have proven it's impossible.
Pi is a mystery, it's a field of research maybe forever. So, you have dozens of ways to approach, to calculate, to cope with this Pi number. One of them is particularly funny, because it connects with probability. This method to calculate Pi was proposed by Monte Carlo. He just put on the ground parallel lines like this. The same distance between 2 lines, let's call it D. Then he took a stick, and the length of the stick was exactly D. That's all he needed, parallel lines and a stick.
Then he was somewhere in the room, threw the stick and the stick fell on the ground. There are two possibilities: either somehow the stick crosses a line, or it doesn't. Monte Carlo proved that the probability of the stick crossing the line is 2 /π, roughly 2/3.
Incredible. And he was amazing because he made an experiment. He threw the stick 10,000 times to the ground, just taking into account if, yes or no, the stick crossed the line. And he found something like 3.14. That's how in mathematics everything is connected. Probability, Pi, E and many more as we will see in the next videos.
In the next episode, discover how Galileo proved Aristotle wrong by rolling a ball down a slope.
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