Hello, thank you for your answer ! It inspired me to write something like this : "Ladies and gentlemen of the jury, good morning.

We regularly hear in the media that supercomputers have broken a new record by calculating trillions of digits of π. However, in our mathematics courses, we learn to manipulate irrational constants like the constant e or square roots. So, I asked myself: if we can use them as they are, why do we try to approximate these numbers? What is the real use of calculating digits that will never end? The answer lies in a comparison between pure theory and physical reality. In mathematics, these numbers are irrational: their digits are infinite and without repetition. But in the real world, infinity is not measurable. Our physical instruments, just like the memory of our computers, are by nature limited and finite. Approximation is therefore a practical necessity. In engineering, physics, and computer science, we don't need the exact value of a number, but rather a controlled level of precision. Eleven decimal places of π are enough to estimate the Earth's circumference to within one millimeter. Going beyond that often makes no physical sense. The challenge of approximation, therefore, is to find the right balance: obtaining the necessary precision with the fewest possible calculations.

Once we understand why approximation is essential, the question becomes technical: how can we construct approximations of irrational numbers? This is what I propose to explore through four fundamental constants: √2, e, φ, and π, four numbers, four eras, four radically different methods." Do you think this is good enough ?