# #10. Where is the Triangle?

(Back to course page.)

Link to Slides · Link to Video

Prompts for discussion:

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?

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.