let l be a Poincare line and let H be some hypercycle of l. We know that every poincare line that cuts l orthogonally, also cuts H orthogonally. At first glance, it seems that this would produce infinitely many rectangles. Yet, we know that rectangles do not exist in hyperbolic geometry. Explain why this does not produce a contridiction.
let l be a Poincare line and let H be some hypercycle of l. We know that every poincare line that cuts l orthogonally, also cuts H orthogonally. At first glance, it seems that this would produce infinitely many rectangles. Yet, we know that rectangles do not exist in hyperbolic geometry. Explain why this does not produce a contridiction.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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let l be a Poincare line and let H be some hypercycle of l. We know that every poincare line that cuts l orthogonally, also cuts H orthogonally. At first glance, it seems that this would produce infinitely many rectangles. Yet, we know that rectangles do not exist in hyperbolic geometry. Explain why this does not produce a contridiction.
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