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Does there exist a regular simple closed curvey in the plane with total curvature less than 2, i.e. such that √, k ds < 2? Select one: O a. Yes, there exists such a curve. In fact, there exists a curve with these properties with constant curvature. O b. Yes, there exists such a curve, but any such curve has non-constant curvature. O c. Yes, there exists such a curve, but any such curve is not convex. No, no such curve exists, by the Jordan curve theorem. O d. O e. No, no such curve exists, by Hopf's Umlaufsatz. O f. No, no such curve exists, by Fenchel's theorem. g. No, no such curve exists, by the isoperimetric inequality. No, no such curve exists, by Green's theorem. No, no such curve exists, by the four vertex theorem. O j. No, no such curve exists, by Gauss' Theorema Egregium. Ok. No, no such curve exists, by the Gauss-Bonnet theorem. Oh. O i.

Does there exist a regular simple closed curvey in the plane with total curvature less than 2, i.e. such that √, k ds < 2? Select one: O a. Yes, there exists such a curve. In fact, there exists a curve with these properties with constant curvature. O b. Yes, there exists such a curve, but any such curve has non-constant curvature. O c. Yes, there exists such a curve, but any such curve is not convex. No, no such curve exists, by the Jordan curve theorem. O d. O e. No, no such curve exists, by Hopf's Umlaufsatz. O f. No, no such curve exists, by Fenchel's theorem. g. No, no such curve exists, by the isoperimetric inequality. No, no such curve exists, by Green's theorem. No, no such curve exists, by the four vertex theorem. O j. No, no such curve exists, by Gauss' Theorema Egregium. Ok. No, no such curve exists, by the Gauss-Bonnet theorem. Oh. O i.

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.
Chapter7: Locus And Concurrence
Section7.1: Locus Of Points
Problem 2E: Note: Exercises preceded by an asterisk are of a more challenging nature. In the figure, which of...
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Does there exist a regular simple closed curve y in the plane with total curvature less than 2, i.e. such that √¸ ñ ds < 2à ? Select one: O a. Yes, there exists such a curve. In fact, there exists a curve with these properties with constant curvature. O b. Yes, there exists such a curve, but any such curve has non-constant curvature. C. Yes, there exists such a curve, but any such curve is not convex. O d. No, no such curve exists, by the Jordan curve theorem. O e. No, no such curve exists, by Hopf's Umlaufsatz. O f. No, no such curve exists, by Fenchel's theorem. g. No, no such curve exists, by the isoperimetric inequality. O h. No, no such curve exists, by Green's theorem. O i. No, no such curve exists, by the four vertex theorem. O j. No, no such curve exists, by Gauss' Theorema Egregium. Ok. No, no such curve exists, by the Gauss-Bonnet theorem.
Transcribed Image Text:Does there exist a regular simple closed curve y in the plane with total curvature less than 2, i.e. such that √¸ ñ ds < 2à ? Select one: O a. Yes, there exists such a curve. In fact, there exists a curve with these properties with constant curvature. O b. Yes, there exists such a curve, but any such curve has non-constant curvature. C. Yes, there exists such a curve, but any such curve is not convex. O d. No, no such curve exists, by the Jordan curve theorem. O e. No, no such curve exists, by Hopf's Umlaufsatz. O f. No, no such curve exists, by Fenchel's theorem. g. No, no such curve exists, by the isoperimetric inequality. O h. No, no such curve exists, by Green's theorem. O i. No, no such curve exists, by the four vertex theorem. O j. No, no such curve exists, by Gauss' Theorema Egregium. Ok. No, no such curve exists, by the Gauss-Bonnet theorem.
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