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Brachistochrone: A Multiversal Tale

Audience:

This video aims to intuitively explain about Brachistochrone or cycloid curve in a fun way. While mathematical details are included, they can be skipped without losing the main ideas.

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4.99 Overall score*

91 Rank

6 Votes

5 Comments

Comments

Brachistochrone my beloved. Great video with both the history and the mathematics.

I visited the Netherlands last year, and made a stop at Huygens’ house in Voorburg. There’s a pendulum in there, maybe a subtle reference to Christiaan Huygens and the Tautochrone problem (very related to the Brachistochrone problem). Worth a visit! :D

For people who want to study this problem in depth, this was certainly a very rich and detailed presentation.

4.3

I think having an intro conceit with the new universe was good and my favorite part was the visual explanation of the ICOR. I think the explanation of the problem and what the multiverse was could have been clearer.

Its a nice touch to have the song on the brachistocrhone.

This video seems tailored to an audience further in their math education than high schoolers as it was tagged due to its inclusion of operations that aren’t typically covered in a high school education like line integrals, partial derivatives, and the Euler-Lagrange equation that needed to be further explained. Parts of the video where simplifcation/derivation of an equation is done could have been longer or explained in further depth because they were hard to follow at times. The Cycloidal Love section seemed out of place with the rest of the video. The volume of the video should be adjusted higher, especially since the Cycloidal Love song is twice as loud as the teaching portion of the video.

At 6:13 I feel there could have been more steps shown for the simplifcation between $\left(\frac{\sin \theta}{1-\cos \theta}\right)^2 + 1$ and $\frac{2}{1-\cos \theta}$ since it’s not immediately obvious how the right side comes from the left side due to several identities and expansions needing to be applied between the steps. At 11:05 the derivation of the parametric equation could have been explained in further depth; currently, it is hard to follow and seems like it was just skimmed over due to the derivation being on screen for a total of three seconds before moving on the next topic.

16:23 What is the Euler Lagrange Equation?

The equations were hard to follow but I liked the visuals (and the song)