# Closed plane curve

## 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?

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## Answers and Replies

haruspex
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Gold Member
Is it allowed to cross itself?

since it is not convex I think it can cross itself.

Ray Vickson
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Dearly Missed

## 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?

A banana curve does not have positive curvature everywhere.

Ray - You are right! So how can I draw one that is positive curvature?

Ray Vickson
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Dearly Missed
Ray - You are right! So how can I draw one that is positive curvature?

Well, that is your assignment!

Can you give a hint please?

If it were convex then it is just a sphere? But a non-convex with positive curvature is confusing me.

LCKurtz
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Gold Member
Can you give a hint please?

If it were convex then it is just a sphere? But a non-convex with positive curvature is confusing me.

You mean "circle". You were given a hint -- let the curve cross itself. Try it.

Yup, I am meant circle. Will an number 8 satisfy it where the top is a bit more curved?

LCKurtz
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Gold Member
No. As soon as you start curving the other way your curvature goes through zero.

Wow, this is harder than I thought.

So it must cross itself? Am I overthinking this?

LCKurtz