Draw a Closed Plane Curve w/ Positive Curvature

In summary, the conversation discusses how to draw a closed plane curve with positive curvature that is not convex. The individual suggests drawing it like a curved banana, but it is pointed out that a banana curve does not have positive curvature everywhere. The conversation then discusses the possibility of the curve crossing itself, and it is determined that this is allowed. The individual is given a hint to try drawing a curve that crosses itself, and it is mentioned that a circle would satisfy the conditions if it were convex. The conversation concludes with the individual realizing that the curve must cross itself and mentioning that it is harder than they initially thought.
  • #1
Lee7
19
0

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?
 
Last edited:
Physics news on Phys.org
  • #2
Is it allowed to cross itself?
 
  • #3
since it is not convex I think it can cross itself.
 
  • #4
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?

A banana curve does not have positive curvature everywhere.
 
  • #5
Ray - You are right! So how can I draw one that is positive curvature?
 
  • #6
Lee7 said:
Ray - You are right! So how can I draw one that is positive curvature?

Well, that is your assignment!
 
  • #7
Can you give a hint please?
 
  • #8
If it were convex then it is just a sphere? But a non-convex with positive curvature is confusing me.
 
  • #9
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.

You mean "circle". You were given a hint -- let the curve cross itself. Try it.
 
  • #10
Yup, I am meant circle. Will an number 8 satisfy it where the top is a bit more curved?
 
  • #11
No. As soon as you start curving the other way your curvature goes through zero.
 
  • #12
Wow, this is harder than I thought.
 
  • #13
So it must cross itself? Am I overthinking this?
 
  • #14
It isn't hard; it's almost trivial. Take a pencil and start drawing. Don't change curvature direction, use the hint, and close the curve.
 

What is a closed plane curve with positive curvature?

A closed plane curve with positive curvature is a shape that is defined by a continuous line that forms a loop or closed shape on a flat surface. It has a positive curvature, meaning that at any point on the curve, the direction of the curve is concave or outward.

What is the difference between positive and negative curvature?

Positive curvature is when the curve bends outward, while negative curvature is when the curve bends inward. In other words, positive curvature has a convex shape while negative curvature has a concave shape.

What are some real-life examples of closed plane curves with positive curvature?

Some examples of closed plane curves with positive curvature include circles, ovals, and ellipses. These shapes can be found in nature, such as the shape of a flower or an egg, or in man-made objects like a clock or a wheel.

How is positive curvature measured?

Positive curvature is measured by the radius of curvature at a specific point on the curve. The larger the radius, the smaller the curvature and vice versa. Positive curvature can also be measured by the angle formed by the tangent lines at two points on the curve.

What are the applications of studying closed plane curves with positive curvature?

The study of closed plane curves with positive curvature has many applications, including in fields such as engineering, architecture, art, and physics. Understanding positive curvature can help in creating stable and efficient designs, as well as in analyzing the behavior of physical systems and structures.

Similar threads

Replies
8
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
348
Replies
4
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
4
Views
966
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
2K
  • Calculus and Beyond Homework Help
Replies
3
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
Back
Top