Name: Problems Plus 7: Calculating π Using the Formula of John Machin (1680 - 1751)
Uploaded: 2023-09-15T03:26:39+00:00
Duration: 1 h 1 min 54 s
Description: In this video I go over a very long problem that involves first determining several arctan formulas and then using them to determine the value of the π up to 7 decimal places. One such formula is name

2 years ago

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math calculus science trigonometry trig arctan inverse tan pi calculating pi mathematics taylor series

In this video I go over a very long problem that involves first determining several arctan formulas and then using them to determine the value of the π up to 7 decimal places. One such formula is named after mathematician John Machin (1680 - 1751) whom used it to determine π correct to 100 decimal places well before the invention of computers. This method also involves using the Maclaurin series for arctan or inverse tan which I had derived in my earlier videos. With modern computers however, the value of π has been calculated to trillions of decimal places!

The timestamps of key parts of the video are listed below:

- Problem 7: 0:00
- Solution to Part (a): 2:10
- Solution to Part (b): 16:42
- Solution to Part (c): 24:24
- Solution to Part (d): 38:00
- Solution to Part (e): 50:06
- Solution to Part (f): Calculating π: 55:58

This video was taken from my earlier video listed below:

- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P