Recently, 3blue1brown shared a video going quite in depth a…
Recently, 3blue1brown shared a video going quite in depth and detail about this exact question and some related equations and concepts. I really like this video, so if the subject interests you, give it a try.
https://www.youtube.com/watch?v=fsLh-NYhOoU
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At the end of the above video, Grant, the host from 3blue1brown, shares this video puzzle he did for Numberphile several years back.
In the video, he goes in depth and detail about ways to consider analogies to the concept of the volume of higher-dimensional balls as being similar to the concept of 2-dimensional concentric success cases for the squares of arbitrary complex points.
This is a really interesting and helpful way to deconstruct the concept of higher-dimensional modeling, and it somewhat emphasizes the concept of higher-dimensional models being dependent on reflections of lower-dimensional structures.
You can watch this video involving an imaginary game of darts and their analogy to higher-dimensional structures here:
https://www.youtube.com/watch?v=6_yU9eJ0NxA