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comment Lie and Weierstrass' visualization of complex functions
Over the weekend, I thought up a construction similar to yours. To a complex number $x+iy$ in the functions argument I associate the line connecting $(0,0,-1)$ and $(x,y,0)$. An upward unit vector in the direction of this line acts like your $v$. Like you, I map this line to a member of its orthogonal complement of parallel lines. I orient this complementary space using a vector in the direction of the real axis original complex plane (instead of $n$). But I also have difficulty seeing how this collection of lines in three space provides insight into the behavior of a complex function.
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comment Lie and Weierstrass' visualization of complex functions
I am with you as far as you went, but what then? Something involving a map from the Riemann sphere, as lines, to all the lines in 3-space? Nothing I thought of made much sense. Certainly nothing provided any insight into the function being modeled.
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comment Lie and Weierstrass' visualization of complex functions
@deoxygerbe The quote is on page 41 in either the third (1920) or fourth (1927) edition — the first section of the third chapter.
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