The article delves into a geometric thought experiment involving n-balls in high dimensions, showcasing the complex nature of these shapes. Starting in 2D with a square holding four circles, the construct evolves into 3D and beyond, revealing surprising revelations. As dimensions increase, the red ball expands exponentially, eventually protruding outside the enclosing box. The volume calculations lead to intriguing conclusions, such as the ball surpassing the box’s volume in higher dimensions. The visual representations help build intuitions about the intricate nature of high-dimensional constructs, challenging conventional perceptions. The mind-bending concepts explored in this article push the boundaries of mathematical imagination.
https://www.arnaldur.be/writing/about/an-n-ball-between-n-balls