Скачать или смотреть No Cuboid has an Equal Volume, Surface Area and Perimeter. Here's why.

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"The Impossible Cuboid"
In this video, I discuss a proof of the fact that a cuboid can't have an equal volume, surface area, and perimeter (at least in the real world!). We motivate the solution by considering a simpler version of the problem and go back into 3D.

As an aside, I'm extremely happy about how the animations have come out in this video (you can even watch it in 4K). For those of you curious, I made the entire video using the free version of Davinci Resolve. The next improvement I plan on doing will be my microphone (as many of you have pointed out).

This video supplements my entry to the "Tom Rocks Maths essay competition"

(Yes, I did miss a minus sign at 10:34; the equation really is infamous)

Also, when the cubic discriminant = 0, it should say repeated real roots rather than 2 real roots (thanks to the comment pointing that out)

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Chapters:
0:00 Introduction
0:49 Simplification
2:32 Roots of Polynomials
5:54 Main Problem
12:17 Final Thoughts



Music:
Yehezkel Raz - Ballerina
Yonatan Riklis - Tales of the Mind
Adrien de la Salle - Shimmer