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Richard Muller,

Updated Dec 2 · Upvoted by Pedro Henrique Bernardinelli, Physics PhD student and Shankar Iyer, Ph.D. in Condensed Matter Theory from Caltech

When I first heard of square seconds, my mind boggled and my learning almost came to an end. It took a while, but I finally figured it out. Now I teach about them.

It’s easier to understand if, instead of meters per second, you talk in terms of miles per hour. You start at rest. After one second, you are going 1 mph. A second later you are going 2 mph. A s...

(more)Alon Amit,

Written Jun 20 · Upvoted by Alberto Bietti, MS in Applied Math, Ecole Normale Supérieure and Igor Markov, MA in Mathematics, PhD in CS

The first known attempt at answering this question is in a letter written by Daniel Bernoulli on October 26, 1729. That’s **287 years ago**. (See “Why is the Gamma function so [*sic*] as it is?” By Detlef Gronau [1].)

Bernoulli used a formula which, in modern notation, would be written as

[math]\displaystyle n! = \lim_{k \to \infty} \left(k+1+\frac{n}{2}\right)^{n-1} \prod_{i=1}^k \frac{i+1}{i+n}[/math].

In the letter, Bernoulli tried to estimate [math]\frac{3}{2}![/math] using this limit, and got a va...

(more)Wait, what? What do you mean, "what is [math]\pi[/math]"? It's the ratio of the circumference of a circle to its diameter. Or it's the area of a circle of radius 1, or something like that. Ever...

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