# Fundamental Math Constants

## Name

Name Symbol Value
Archimedes' constant or Ludolph's number.
Pi.
$\pi\,\!$ $\lim_{n \to \infty}\frac{P_{n}}{d}\,\,$

$\approx 3.14159\,\,26535\,\,89793\,\,23846\,\,26433\,\,83279\,\,50288\,\,41971\,\,\!$
Napier's constant.
Base of Natural Logarithms.
$e \,\!$ $\lim_{n\to\infty} \left(1+{1\over n}\right)^n\,\,$

$\approx 2.71828\,\,18284\,\,59045\,\,23536\,\,0287\,\!$
Pythagoras' constant.
Square root of two.
$\sqrt {2} \,\!$ $\approx 1.41421\,\,35623\,\,73095\,\,04880\,\,16887\,\,24209\,\,69807\,\,85696\,\,71875\,\,37694\,\!$
Theodorus' constant.
Square root of three.
$\sqrt {3} \,\!$ $\approx 1.73205\,\,08075\,\,68877\,\,29352\,\,74463\,\,41505 \,\,87236\,\!$
Euler-Mascheroni's constant.
Gamma.
$\gamma\,\!$ $\lim_{n \rightarrow \infty } \left[ \left( \sum_{k=1}^n \frac{1}{k} \right) - \ln(n) \right]$

$\approx 0.57721\,\,56649\,\,01532\,\,86060\,\,6512$
Apéry's constant..
Zeta(3)
$\zeta(3)\,\!$ $\sum_{k=1}^\infty\frac{1}{k^3}=1+\frac{1}{2^3} + \frac{1}{3^3} +\frac{1}{4^3} +\frac{1}{5^3} +\ldots$

$\approx 1.20205\; 69031\; 59594\; 28539\; 97381\;61511\,$
The Golden Ratio.
Phi
$\varphi\,\!$ $\frac{1+\sqrt{5}}{2}$

$\approx 1.61803\,\,39887\,\,$
Natural logarithm of two. $ln2\,\!$ $\sum_{k=1}^\infty\frac{(-1)^{k-1}}{k}=1+\frac{-1}{2} + \frac{1}{3} + \frac{-1}{4} + \frac{1}{5} + \ldots\,$

$\approx 0.69314\;71805\;59945\;30941\,72321\;21458\;17656\,$
Delian's constant.
Cube root of two.
$\sqrt[3] {2}\,\!$ $\approx 1.25992\;10498\;94873\;16476\;72106\;07278\;22835\;$

## Usage

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# Web Resources

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