That was very good (thank you!), but it led me to this, which was even better:

https://www.youtube.com/watch?v=rAHcZGjKVvg

I wish more of mathematics was visual. That's the mode of thinking I employ the most, and I excel at spatial problems.

I wish higher level mathematics and physics paid more attention to the use of visual schematics and diagrams. So much can be communicated with them. Words often pale in comparison.

I would like to recommend the 3b1b's[1] YouTube channel.

His procedurally generated videos really make you think of certain math that looked unintuitive or hard to explain in a truly intuitive, visual way.

His series on linear algebra was very eye opening to me, as well as many of his videos about subjects I was initially failing to understand.

[1] https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw

Thanks so much for sharing! This looks fantastic.

drop https://m.youtube.com/watch?v=lt-zvsGvtqg

After watching the video, I feel like this follows intuitively from the fact that sqrt(2) > 1.

The biggest possible difference between Prince Rupert's cubes is 3%, which is much smaller than the difference between sqrt(2) and 1.

FWIW, `(sqrt(2)-1)^3` is `0.071067831`, which while not equal to `(1.0606601-1)` is fairly close.