Does there exist a regular closed curve in the plane with exactly 2 vertices? 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. No, no such curve exists, by the Jordan curve theorem. O d. No, no such curve exists, by Hopf's Umlaufsatz. O e. No, no such curve exists, by Fenchel's theorem. O f. No, no such curve exists, by the isoperimetric inequality. g. No, no such curve exists, by Green's theorem.
Does there exist a regular closed curve in the plane with exactly 2 vertices? 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. No, no such curve exists, by the Jordan curve theorem. O d. No, no such curve exists, by Hopf's Umlaufsatz. O e. No, no such curve exists, by Fenchel's theorem. O f. No, no such curve exists, by the isoperimetric inequality. g. No, no such curve exists, by Green's theorem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Does there exist a regular closed curve in the plane with exactly 2 vertices?
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. No, no such curve exists, by the Jordan curve theorem.
O d.
No, no such curve exists, by Hopf's Umlaufsatz.
O e. No, no such curve exists, by Fenchel's theorem.
O f. No, no such curve exists, by the isoperimetric inequality.
g.
No, no such curve exists, by Green's theorem.
O h.
O i.
No, no such curve exists, by the four vertex theorem.
No, no such curve exists, by Gauss' Theorema Egregium.
O j. No, no such curve exists, by the Gauss-Bonnet theorem.
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