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archimedes_constant_π [2013/09/12 13:34] nikolaj |
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| ===== Archimedes constant π ===== | ===== Archimedes constant π ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| 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 $\mathbb E^2$: | 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 $\mathbb E^2$: | ||
| - | | @#FFBB00: $\pi:=V_2(1)$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\pi:=V_2(1)$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| * $\pi \approx \frac{22}{7}$ | * $\pi \approx \frac{22}{7}$ | ||
| - | === 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 === | === Reference === | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Pi|Pi]] | + | Wikipedia: [[http://en.wikipedia.org/wiki/Pi|Pi]],[[http://en.wikipedia.org/wiki/List_of_formulae_involving_%CF%80|List of formulae involving π]] |
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Ball volume]], [[Euclidean space]] | [[Ball volume]], [[Euclidean space]] | ||
