Area between two closed curves

In summary, the person has been searching for a solution to finding the area of intersection between two general closed loops. They were hoping to get assistance from the community and provided an image and equations for reference. They also mentioned that the process becomes more complex if there are multiple intersections.
  • #1
SSGD
49
4
I have been trying to find an answer to this problem for some time. So I was hoping the community might be able to point me in the right direct.

https://drive.google.com/open?id=1Y2hYkRG94whLroK20Zmce07jslyRL3zZ

I couldn't get the image to load. So above is a link to an image of the problem. I am trying to find a general solution to the intersection of the two general closed loops.

In the image Ai and Aj are just the area of each closed loops and Aij is the area of the intersection of the two closed loops. ri and rj are just parameterizations of the positions around the closed loop.

Their is a general equation for the area of a closed loop defined by a line integral and I was wondering if there might be a line integral for the area of intersection between two closed loops.
 
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  • #2
You can find the boundary of the overlap area by finding the intersections between the two boundaries and combining the sections between them to form a new line.
If there is an infinite set of intersections or similar things get more complicated.
 

1. What is the definition of "area between two closed curves"?

The area between two closed curves refers to the region enclosed by two curves on a plane, where the curves intersect or are connected at their endpoints.

2. How is the area between two closed curves calculated?

The area between two closed curves can be calculated by finding the integral of the difference between the two curves with respect to the variable of the curves. This can be done using various methods such as the disk method, the shell method, or by splitting the region into smaller sections.

3. What is the significance of calculating the area between two closed curves?

Calculating the area between two closed curves is useful in many applications, such as determining the area of a region on a map, finding the volume of irregular shapes, or analyzing the area under a curve in mathematics and physics.

4. Can the area between two closed curves be negative?

No, the area between two closed curves cannot be negative. It is always a positive value as it represents the magnitude of the enclosed region.

5. Are there any real-life examples of the area between two closed curves?

Yes, there are many real-life examples of the area between two closed curves, such as finding the area of a lake or pond on a map, calculating the volume of a swimming pool, or determining the area under a velocity-time graph in physics to find the displacement of an object.

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