Does there exist a regular simple closed curvey in the plane with total curvature less than 2, i.e. such that ſy ñ ds < 2π ? 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. O d. No, no such curve exists, by the Jordan curve theorem. Oe. No, no such curve exists, by Hopf's Umlaufsatz. O f. No, no such curve exists, by Fenchel's theorem. O g. No, no such curve exists, by the isoperimetric inequality. Oh. 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 exists, Gauss' Theorema Egregium. Ok. No, no such curve exists, by the Gauss-Bonnet theorem.
Does there exist a regular simple closed curvey in the plane with total curvature less than 2, i.e. such that ſy ñ ds < 2π ? 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. O d. No, no such curve exists, by the Jordan curve theorem. Oe. No, no such curve exists, by Hopf's Umlaufsatz. O f. No, no such curve exists, by Fenchel's theorem. O g. No, no such curve exists, by the isoperimetric inequality. Oh. 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 exists, Gauss' Theorema Egregium. Ok. No, no such curve exists, by the Gauss-Bonnet theorem.
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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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 < 2?
Select one:
a. Yes, there exists such a curve. In fact, there exists a curve with these properties with constant curvature.
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.
d.
No, no such curve exists, by the Jordan curve theorem.
e.
No, no such curve exists, by Hopf's Umlaufsatz.
No, no such curve exists, by Fenchel's theorem.
g.
No, no such curve exists, by the isoperimetric inequality.
Oh.
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.
O f.
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