This is an old revision of the document!
Archimedes constant π
Definition
The constant $\pi$ is defined as the volume of the disc of radius $1$, where the underlying metric space is taken to be the two dimensional Euclidean space $\mathbb E^2$:
| $\pi:=V_2(1)$ |
Discussion
- $\pi = 3.14159\dots$
- $\pi \approx \frac{22}{7}$
Theorems
| $\frac{\pi}{4}=\int_{0}^{1}\frac{1}{1+x^2}\mathrm d x=\sum_{k=0}^\infty \frac{(-1)^k}{2k+1}$ |
|---|
Reference
Wikipedia: Pi
Parents
Requirements
