#10. Where is the Triangle?

Published

11 Nov, 2023

(Back to course page.)

Link to Slides · Link to Video

Prompts for discussion:

  1. Can we generalize the construction for \(d = 3\) to 10 equiangular lines in \(\mathbb{R}^4\)? What’s the best general construction that we can come up with?

  2. With \(n\) lines in \(\mathbb{R}^2\), what’s the largest number of pairs that we can show to have the same angles? For example, with \(n = 4\), we can get 4 pairs to have the same angle; can we get 5?

PS. Although I was quite sure I went “live” on Youtube, I am unable to locate the recording of the session :( I re-recorded it separately, and that’s the link in this post.

PPS. The slides are updated with the \(\mathbf{x}^T M \mathbf{x}\) calculation, which makes more explicit that \(M\) is positive definite.