“All human beings are born free and equal…” but not numbers
Date(s) : 27/11/2025 iCal
17h00 - 18h00
Abstract: This is the story of a date between two real numbers, Alpha and Phi. Alpha introduces themselves succinctly, and within two minutes they have already laid out an almost complete picture of their personality. As a good rational number, Alpha try to get to know their mysterious interlocutor a little better:
“So, are you more rational or irrational?”
Phi, faced with this rather odd question, frowns slightly and replies:
“I find your way of seeing things very binary. It’s a bit reductive to place people into only two categories when numbers are so diverse!”
Alpha then feels a bit silly and, in a slightly embarrassed tone, continues:
“Alright, I see—but you have to be one of the two, because if you’re not one, then you’re the other!”
Phi rolls their eyes and retorts:
“Has it never occurred to you that some of us are more irrational than others? I even have friends who don’t let themselves be easily approached by simple rational numbers! As for me, I am the most irrational of all irrational creatures—and I can prove it!”
And so Phi plunged Alpha into the wonderful adventure of Diophantine approximation. Until then, Alpha had been used to approaching irrationals in a direct way, by spelling out their decimal expansions—but it must be admitted that irrationals quickly grew tired of that unoriginal approach. Phi, however, was more subtle: by using continued fractions, they showed Alpha a far more efficient way to approach irrational numbers (which greatly piqued Alpha’s interest). Finally, Phi showed that there exists a measure of irrationality that makes it possible to classify irrational numbers—and even that some of them have an infinite measure of irrationality!
Emplacement
Luminy - salle 500-504b
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