Revision as of 01:03, 11 May 2016

In this worksheet we study the convergence behavior of the series:

$\sum_{i=1}^{\infty} \dfrac{1}{n^2} = \dfrac{\pi^2}{6}$

Explore a couple of methods of calculating pi, compare the results of a few methods, compare the computational cost. Push the limits.

Incorporate some kind of timing, I don't know.

Variables: number of terms, amount of time, and amount of accuracy.

Worksheet Questions

For each method implemented, calculate pi using 100, 1k, and 10k terms in the series.

Proving the series converges (multiple ways): https://www.youtube.com/watch?v=9euTxoCC8Hk

Link to all worksheets idea list: Worksheets

Calc II:

Calc III:

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 Variables: number of terms, amount of time, and amount of accuracy.
-Implement the following methods of calculating Pi using a for loop.
+=Worksheet Questions=
-For each method implemented, calculate Pi using 100, 1,000, and 10,000 terms in the series.
+* Implement (2) methods of calculating pi using a for loop.
-For each calculation, calculate the absolute error and calculate the amount of time the calculation took.
+* For each method implemented, calculate pi using 100, 1k, and 10k terms in the series.
+* Calculate the absolute error and clock time of each calculation.
+* Create a plot of degree of accuracy versus number of terms. Use a log-log plot.
+* Why does the plot from the previous question require log scales?
 =References=