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January 28th, 2019, 01:31 AM   #1
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Example of properties that the circle unit hasn't

What are the properties the unit circle hasn't, but that ellipses have?

Last edited by skipjack; January 28th, 2019 at 08:16 AM.
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January 28th, 2019, 02:17 AM   #2
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Since the unit circle IS an ellipse, you won't find any property that is common to all ellipses and not the unit circle.
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January 28th, 2019, 08:20 AM   #3
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Perhaps "ellipses other than the unit circle" was intended.
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January 28th, 2019, 08:25 AM   #4
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Perhaps.
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January 28th, 2019, 12:15 PM   #5
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Quote:
Originally Posted by shaharhada View Post
What are the properties the unit circle hasn't, but that ellipses have?
Same as: what are properties that ellipses have but circles don't have ?
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January 28th, 2019, 01:30 PM   #6
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An ellipse has two different axes.

If a planet is in orbit around the sun and it is an ellipse, the sun is at a focus, not at the center. For a circle, there is only one focus at the center.

Last edited by skipjack; January 28th, 2019 at 10:14 PM.
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January 28th, 2019, 01:38 PM   #7
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Uhm. Look it up.

From Wikipedia https://en.wikipedia.org/wiki/Ellipse

An ellipse is a curve in a plane surrounding two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse having both focal points at the same location. The shape of an ellipse (how "elongated" it is) is represented by its eccentricity, which for an ellipse can be any number from 0 (the limiting case of a circle) to arbitrarily close to but less than 1.

So, an ellipse that is not a circle does not have a single focal point. Other differences, such as the lack of a radius and the presence of positive eccentricity, follow from the duality of focal points.
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