Problems Plus 7: Calculating π Using the Formula of John Machin (1680 - 1751)

Math Easy Solutions

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 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