- #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:
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.
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.
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.
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.
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.
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.