Equilateral Ellipse - Formula & References

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In summary, the conversation discusses the concept of an "equilateral ellipse" and whether it refers to a circle or a different type of ellipse. The participants search for a formula and references for this term, with one participant finding a paper by Augustus DeMorgan and others referencing older books. They also mention the possibility of it being related to ellipses inscribed with triangles.
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Douglasdc
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I did and exam a while ago and one of the questions asked to find a formula for an "equilateral ellipse". In my mind an equilateral ellipse should be a circle, but it seems I am wrong.

I searched online for the term, but didn't find anything useful. Does anyone know what it is, can find a formula and give me some references?

Thanks,
Douglas.
 
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Thanks Mark. I found the term in some old books as well and they also state that a circle can be called an "equilateral ellipse".
 

1. What is an equilateral ellipse?

An equilateral ellipse is a type of ellipse where all three axes are equal in length, resulting in a symmetrical shape. It is also known as a circular ellipse or a spherical ellipse.

2. How do you calculate the formula for an equilateral ellipse?

The formula for an equilateral ellipse is (x/a)^2 + (y/b)^2 + (z/c)^2 = 1, where a, b, and c are the lengths of the three axes. This formula is similar to the standard formula for an ellipse, but with the addition of the third axis, z.

3. What are some real-world applications of the equilateral ellipse?

Equilateral ellipses are commonly used in physics and astronomy to model the orbits of planets and other celestial bodies. They are also used in engineering and architecture to design symmetrical structures, such as bridges and arches.

4. Are there any references or sources for learning more about equilateral ellipses?

Yes, there are many resources available for learning more about equilateral ellipses. Some recommended sources include textbooks on geometry, online articles and tutorials, and mathematical forums and communities.

5. What is the difference between an equilateral ellipse and a circle?

An equilateral ellipse and a circle are both symmetrical shapes, but they have different formulas and properties. While all points on a circle are equidistant from its center, an equilateral ellipse has three axes and varying distances from its center. Additionally, a circle has a constant radius, while an equilateral ellipse has three different radii.

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