Non euclidian geometry.Independence of the parallel postulate.Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein model, solve:a. For each point (x, y, 0) calculate the parametric equation of the line 1(x,y) (t) that passesthrough the points (0,0,1) and (x, y,0).b. When x² + y² ≤ 1, find the point F(x, y) that is the intersection of l(x,y) (t) with the sphereE.c. Define the function p(x, y,0) = F(x, y), this function identifies the open circle C in the planexy with equation x² + y² < 1 in the lower hemisphere of the sphere E. In what transforms astring in C?

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dius equal quation of he intersec

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter12: Conic Sections

Section12.CR: Chapter Review

Problem 6CC

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Question

Non euclidian geometry.
Independence of the parallel postulate.
Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-
Klein model, solve:
a. For each point (x, y, 0) calculate the parametric equation of the line 1(x,y) (t) that passes
through the points (0,0,1) and (x, y,0).
b. When x² + y² ≤ 1, find the point F(x, y) that is the intersection of l(x,y) (t) with the sphere
E.
c. Define the function p(x, y,0) = F(x, y), this function identifies the open circle C in the plane
xy with equation x² + y² < 1 in the lower hemisphere of the sphere E. In what transforms a
string in C?

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