16
votes
2answers
973 views

Center of mass from the abstract point of view, or could the ancient Greeks invent modern analysis?

This is a very open-ended question, which may or may not have a perfect answer, and for which I have a few ideas but nothing like a clear picture. However, I guess it won't hurt to ask to see if ...
2
votes
1answer
300 views

A question on a special type of function

Suppose I have a function $f$, and positive integers $x$ and $y$ such that $x$ is a square, $x \ne y$ and $y \ne \sqrt{x}$. Now, assume that: $|\frac{f(x)}{y} - \frac{f(y)}{x}| > 2$ ...
13
votes
3answers
924 views

Card game / options pricing / Brownian bridge question

We play a game. I shuffle a deck of cards and start dealing them face up. After any card you can say "stop", at which point I pay you 1 dollar for every red card dealt and you pay me 1 for every black ...