Is there any way of obtaining the area of an ellipse without using calculus?

In summary, to find the area of an ellipse without using calculus, you can use the formula A = π * a * b, where a and b are the lengths of the semi-major and semi-minor axes of the ellipse. Alternatively, you can use the formula A = π * r1 * r2, which only requires measuring the diameters of the ellipse. The formula for finding the area of a circle cannot be used for an ellipse. To approximate the area of an ellipse without using calculus, the Monte Carlo method can be used. However, calculus is typically used to find the area of an ellipse for a more precise and accurate calculation.
  • #1
omoplata
327
2
If so, can I get a hint on how to do it?

I did a text search for a proof in "Conics" by Apollonius, but couldn't find one. If they couldn't prove it without calculus it means they had to wait until at least Newton's time to find the area of an ellipse?
 
Mathematics news on Phys.org
  • #3
Thanks! :)
 

FAQ: Is there any way of obtaining the area of an ellipse without using calculus?

How can I find the area of an ellipse without using calculus?

To find the area of an ellipse without using calculus, you can use the formula A = π * a * b, where a and b are the lengths of the semi-major and semi-minor axes of the ellipse, respectively.

Is there a simpler way to calculate the area of an ellipse?

Yes, you can also use the formula A = π * r1 * r2, where r1 and r2 are the radii of the ellipse. This method is simpler because it only requires measuring the diameters of the ellipse instead of the lengths of the axes.

Can I use the same formula for finding the area of a circle to find the area of an ellipse?

No, the formula for finding the area of a circle (A = π * r^2) cannot be used for an ellipse because the major and minor axes of an ellipse have different lengths.

Is there a way to approximate the area of an ellipse without using calculus?

Yes, you can use the Monte Carlo method to approximate the area of an ellipse without using calculus. This involves randomly generating points within the ellipse and calculating the percentage of points that fall within the ellipse, which can then be used to estimate the area.

Why is calculus typically used to find the area of an ellipse?

Calculus is typically used to find the area of an ellipse because it allows for a more precise and accurate calculation. The area of an ellipse can be found by integrating the ellipse's equation, which takes into account the changing radius at different points along the curve.

Similar threads

B A Simpler Way to Find the Shaded Area?
Replies
1
Views
1K
Troubles with Ellipses (Cartesian -> Polar)
Replies
5
Views
7K
A rather difficult problem: deltoid inscribed into an ellipse
Replies
1
Views
3K
Studying Reading "How to Prove It" right before taking Calculus I -- Question
Replies
9
Views
2K
Finding Area of Shaded Segment in Circle Using Calculus
Replies
6
Views
1K
Kumon Math and Similar Programs
Replies
6
Views
1K
B What unique contributions to math did linear algebra make?
Replies
19
Views
2K
Insights What Are Numbers? - Insights for Beginners
Replies
0
Views
2K
MHB Constraint optimization without using Calculus
Replies
2
Views
3K
Derivation of time period for physical pendula without calculus
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top