The discussion revolves around the challenge of drawing a closed plane curve that maintains positive curvature while not being convex. Participants are exploring the characteristics of such curves and the implications of self-intersection.
The conversation is active, with participants sharing ideas and seeking clarification on the requirements for the curve. Some have offered hints and suggestions, while others express confusion about the relationship between curvature and self-intersection.
There is an ongoing debate about the definitions of convexity and positive curvature, as well as the constraints of the assignment. Participants are grappling with the concept of maintaining positive curvature while allowing for self-intersection.
Lee7 said:Homework Statement
How can I draw a closed plane curve with positive curvature that is not convex
The Attempt at a Solution
I was thinking drawing it like a banana but more curved, will that do?
Lee7 said:Ray - You are right! So how can I draw one that is positive curvature?
Lee7 said:Can you give a hint please?
Lee7 said:If it were convex then it is just a sphere? But a non-convex with positive curvature is confusing me.