Laborious π Calculator
Iteration: 0
π = 0
$$\pi = 2\sum_{k=0}^\infty{\frac{(2k)!}{2^{2k}(k!)^2(2k+1)}}$$
$$\frac{1}{\pi} = \sum_{k=0}^\infty \frac{((2k)!)^3(42k+5)} {(k!)^6 16^{3k+1}}$$
$$\frac{1}{\pi} = \frac{2\sqrt2}{9801} \sum_{k=0}^\infty \frac{(4k)!(1103+26390k)} {(k!)^4 396^{4k}}$$
$$\frac{426880\sqrt{10005}}{\pi} = \sum_{k=0}^\infty \frac{(6k)!(13591409+545140134k)} {(3k)!(k!)^3(-640320)^{3k}}$$
$$\frac{\pi^2}{6} = \sum_{k=1}^\infty\frac{1}{k^2}$$
$$\frac{\pi}{4} = 4\arctan\frac{1}{5} - \arctan\frac{1}{239} \text{, where } \arctan{z} = \sum_{k=0}^\infty\frac{(-1)^kz^{2k+1}}{2k+1}$$
Click Iterate Once to get started. Then keep clicking. Notice how the result slowly converges on 3.14159265358979. If you get tired, you can switch to 10 Times. Then switch from Zeta to Machin and click Iterate Once several times. See how much more quickly it converges? Then try the other algorithms! Note: this app is crippled by the fact that JavaScript only performs 64-bit math. [JavaScript source]