File:Comparison pi infinite series.svg
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Summary
Comparison of the convergence of several historical infinite series for π. Sn is the approximation of after taking n terms. Each subsequent subplot horizontally magnifies the shaded area by 10 times. The lines are merely to connect points of each series; there are no intermediate values between terms.
The series listed are:
- <a href="https://en.wikipedia.org/wiki/Vi%C3%A8te%27s_formula" class="extiw" title="en:Viète's formula">en:Viète's formula</a>
- <a href="https://en.wikipedia.org/wiki/Wallis_product" class="extiw" title="en:Wallis product">en:Wallis product</a>
- <a href="https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80" class="extiw" title="en:Leibniz formula for π">en:Leibniz formula for π</a>
- <a href="https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama#The_value_of_.CF.80_.28pi.29" class="extiw" title="en:Madhava of Sangamagrama">en:Madhava of Sangamagrama#The value of π (pi)</a>
- A series by <a href="https://en.wikipedia.org/wiki/Nilakantha_Somayaji" class="extiw" title="en:Nilakantha Somayaji">en:Nilakantha Somayaji</a> that doesn't seem to have a wikipedia article, but is <a rel="nofollow" class="external text" href="http://www.wikihow.com/Calculate-Pi#Calculate_Pi_Using_an_Infinite_Series_sub">well known</a>,
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 09:23, 6 January 2017 | | 512 × 256 (45 KB) | 127.0.0.1 (talk) | Comparison of the convergence of several historical infinite series for <span class="texhtml">π</span>. <i>S<sub>n</sub></i> is the approximation of after taking <i>n</i> terms. Each subsequent subplot horizontally magnifies the shaded area by 10 times. The lines are merely to connect points of each series; there are no intermediate values between terms. <p>The series listed are: </p> <ul> <li> <a href="https://en.wikipedia.org/wiki/Vi%C3%A8te%27s_formula" class="extiw" title="en:Viète's formula">en:Viète's formula</a> </li> <li> <a href="https://en.wikipedia.org/wiki/Wallis_product" class="extiw" title="en:Wallis product">en:Wallis product</a> </li> <li> <a href="https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80" class="extiw" title="en:Leibniz formula for π">en:Leibniz formula for π</a> </li> <li> <a href="https://en.wikipedia.org/wiki/Madhava_of_Sangamagrama#The_value_of_.CF.80_.28pi.29" class="extiw" title="en:Madhava of Sangamagrama">en:Madhava of Sangamagrama#The value of π (pi)</a> </li> <li> A series by <a href="https://en.wikipedia.org/wiki/Nilakantha_Somayaji" class="extiw" title="en:Nilakantha Somayaji">en:Nilakantha Somayaji</a> that doesn't seem to have a wikipedia article, but is <a rel="nofollow" class="external text" href="http://www.wikihow.com/Calculate-Pi#Calculate_Pi_Using_an_Infinite_Series_sub">well known</a>,</li> </ul> |
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