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:Show that if every point of a surface is elliptic, then any curve C on this surface positive curvature. (Recall that curvature K > 0. Try proof by contradiction.)

:Show that if every point of a surface is elliptic, then any curve C on this surface positive curvature. (Recall that curvature K > 0. Try proof by contradiction.)

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.6: The Three-dimensional Coordinate System
Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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21.b : Show that if every point of a surface is elliptic, then any curve C on this surface will have positive curvature. (Recall that curvature k > 0. Try proof by contradiction.)
Transcribed Image Text:21.b : Show that if every point of a surface is elliptic, then any curve C on this surface will have positive curvature. (Recall that curvature k > 0. Try proof by contradiction.)
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