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
icon
Related questions
Question
100%

Need help with this question. Please explain each step. Thank you :)

 

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.
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.
Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,