In this video I go over a very surprising connection between the centroid of a region and the resulting volume of revolution obtained from it. This connection states that the volume of a shape formed by rotating a region about the line is equal to the area of the region multiplied by distance the centroid of the region travels around the line of revolution. This connection is called the Theorem of Pappus, named after the founder Pappus of Alexandria in the 4th century A.D. This is a remarkable yet surprising connection between volumes and centers of mass because these two topics seem on the surface very different from each other.
As well as the proof of the Pappus Theorem, I also go over a brief math (mainstream) history lesson on Pappus, who was a great Greek mathematician far ahead of his time, so make sure to watch this video!
Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104685&authkey=!AByGvDBNcGgx40k&ithint=file%2cpdf
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-moments-and-centers-of-mass-theorem-of-pappus
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I don't always determine the volume of a shape but when I do I usually solve it using the center of mass ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-moments-and-centers-of-mass-theorem-of-pappus