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Theorem of Borsuk and Ulam (~1930s).
Let n ≥ 1. For each continuous function
F: Sⁿ → Rⁿ
from the n-sphere Sⁿ into n-dimensional Euclidean space Rⁿ, there is a point p∈Sⁿ such that F(p) = F(-p). #math#calculus
@choptopmoseley I had the opportunity to start a Math Help and Special Interest channel on YouTube. I've been wanting to do that for years but having everything transition to Zoom University forced me to buy the tools I needed to also make YouTube videos. I'm stoked!
https://t.co/XFwYZKnSqL
@mrclbschff Hi Marcel, thanks for stopping over!
If A^2 = I then det(A^2) = (det A)^2 = det I = 1. So det A = +1 or -1. If det A = 1, we get x^3 + y^3 + z^3 = 5. If det A = -1, we get x^3 + y^3 + z^3 = 7 our solution from the video.