What would base $1$ be? - Mathematics Stack Exchange The examples given with base 10 and 2 in the question are positional bases In a positional base 1, you only got one digit, with no value: 0 All positions will have zero value, and you can only represent one number: 0 – Bijective base 1 would be one way to make it funcitonal, but that isn't a positional base
Prove that $e^ {i\pi} = -1$ - Mathematics Stack Exchange The $\pi$ itself is defined as the total angle which connects $1$ to $-1$ along the arch Summarizing, we can say that because the circle can be defined through the action of the group of shifts which preserve the distance between a point and another point, the relation between π and e arises