Hacker News new | past | comments | ask | show | jobs | submit login

These observations have a bit of the flavor of the birthday paradox and pigeonhole principle: if the size of a certain object is at least so and so, then a certain property is guaranteed. If we have more than 365 people, then a birthday has to repeat.

Also, the Mean Value Theorem comes to mind for some reason.

The mean value theorem also guarantees existence (of a parallel line tangent).

Guidelines | FAQ | Support | API | Security | Lists | Bookmarklet | Legal | Apply to YC | Contact