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Bonus footage from Ellipse Perimeter video. (Patreon)

Published:
2020-09-05 15:34:39
Imported:
2026-06

Content

This starts with some bonus patreon footage I deliberately filmed. You can see it exactly flows off a shot from the main video (although I later had to extend the pause in the main video when I decided afterward to add a "total ellipse of the chart" there). This is me talking about why my approximations are so different for ellipses which are very close to being circles.

And then there is a deleted scene which was going to be in the main video but I decided to take it out at the last minute. It talks about how for extreme ellipses the perimeter approaches 4a. My lazy approximation approaches (5π/6)a which means there is an upper bound on the percentage error. 

Main video is here: https://youtu.be/5nW3nJhBHL0

Files

BONUS: perimeter of an ellipse extra footage

Here is both an extra Patreon message from me to thank all my supporters as well as a "deleted scene" which was cut from the main video. https://www.patreon.com/posts/41274351 Main video is over here: https://youtu.be/5nW3nJhBHL0

Comments

DrDelvan

When choosing coefficients, the most beneficent is not the most efficient, but indeed those that look neat.

David Perek

Well, 3,4,5, and 6 are definitely easy to remember! For a lot of problems in engineering, we'd ideally have a multi-axis sensor which would read with a gain of 1.0 and offset of 0.0, and each axis having cos(theta) and sin(theta) of the signal(and so on in 3d), like for triaxial accelerometers and magnetometers. So ellipses and ellipsoids are a natural fit for a regression to come up with calibration parameters...but of course unless you have a lousy sensor, the eccentricity is hopefully close to 1! I bet Kepler was in the same boat. But I bet if the kids could learn how to use linear algebra to fit an ellipse or ellipsoid, they'd be ready to take a lot of good jobs, including maybe mine!

Kristian Joensen

I have good memories working with ellipses in math class in the final year of high school. Fun times. Although many of the things from those days are rusty. But some of it came back to me from watching this video.