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## 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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- Thread starter Lee7
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- #1

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How can I draw a closed plane curve with positive curvature that is not convex

I was thinking drawing it like a banana but more curved, will that do?

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- #2

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Is it allowed to cross itself?

- #3

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

- #4

Ray Vickson

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## 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.

- #5

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

- #6

Ray Vickson

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

Well, that is your assignment!

- #7

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Can you give a hint please?

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- #9

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Can you give a hint please?

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

- #10

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

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

- #12

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Wow, this is harder than I thought.

- #13

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So it must cross itself? Am I overthinking this?

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