Area of an ellipse and similar problems

In summary, the conversation discusses the method for finding the area of an ellipse by breaking it into infinitesimally small triangles and integrating. The question is raised about why not using infinitesimally small circle segments instead, as both methods seem to have equal logical merit but produce different results. The speaker also mentions other problems regarding integration of geometric objects and questions the governing factor in choosing between the two methods.
  • #1
Gauss M.D.
153
1
To find the area, you break the ellipse into infinitesimaly small triangles and integrate.

But why? Why not break it up into infinitesimaly small circle segments and calculate it through circumference instead?

There are other problems regarding integration of geometric objects that has me wondering the same thing. Integrating a function in polar coordinates for example. It seems to me that the triangle method and the circle method has equal logical merit. But one of them produces the wrong result. What's governing which one to choose?
 
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  • #2
Could you put your circle segment idea in mathematical terms? I am sure that it works if you do it right.
 

1. What is the formula for finding the area of an ellipse?

The formula for finding the area of an ellipse is A = π * a * b, where a and b are the lengths of the semi-major and semi-minor axes, respectively.

2. How is the area of an ellipse different from a circle?

The area of an ellipse is different from a circle because a circle has equal lengths for its major and minor axes, while an ellipse has different lengths for its major and minor axes.

3. Can the area of an ellipse be negative?

No, the area of an ellipse cannot be negative. The area of a shape is always a positive value.

4. How do you find the area of an ellipse if only the circumference is given?

If only the circumference of an ellipse is given, the area can be found using the formula A = (c/2π)^2 * π * a * b, where c is the circumference and a and b are the lengths of the semi-major and semi-minor axes, respectively.

5. Can the area of an ellipse be greater than the area of a circle with the same circumference?

Yes, the area of an ellipse can be greater than the area of a circle with the same circumference. This is because the lengths of the semi-major and semi-minor axes can vary, resulting in different areas for an ellipse with the same circumference as a circle.

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