#10. Where is the Triangle?

(Back to course page.)

Link to Slides · Link to Video

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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?

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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.