We review the basic connection between hyperbolic points and matrices, and connect the J function, which computes the joins of points or the meets of lines, with the Lie bracket of 2x2 matrices. This connects with the Lie algebra called sl(2) in the projective setting. The Jacobi identity then gives a new proof of the concurrence of the altitudes of a triangle, in other words the existence of the orthocenter.
"... physics and other branches of mathematics" i knew it: mathematics > physics :)
or in other words: reality is just one of many things we can imagine
btw: thanks for all your videos on youtube, keeping me close to subjects of mathematics. a big treasure for those who lost connection with academic life but still are interested!
TheRealSeus 5 months ago