# Talk:Ellipse

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## Numerical and linear eccentricity

Unfortunately, nowadays there is a confusion in notation. Traditionally the linear eccentricity should be denoted with the latin e, and the numerical eccentricity should be denoted with the greek ε, where e=εa. Even on this page there is an obvious confusion in notation.Theodore Yoda (talk) 15:29, 25 March 2013 (UTC)

## Polar angle

### Parametric form in canonical position, missing angles in drawing

I agree with the archived comment requesting labels on the diagramme http://en.wikipedia.org/wiki/File:Parametric_ellipse.gif. —DIV (138.194.10.62 (talk) 06:54, 12 May 2013 (UTC))

### Accuracy of formula

Mathworld seems to have a different formula as their #58 compared to Ellipse#Parametric_form_in_canonical_position. I think WP is correct, but am puzzled at the discrepancy. —DIV (138.194.10.62 (talk) 06:55, 12 May 2013 (UTC))

## Etymology

Quoth The name ἔλλειψις was given by Apollonius of Perga in his Conics, emphasizing the connection of the curve with "application of areas".

I don't get this sentence. Is an ellipse called so because it's a defective circle?

Thanks, Maikel (talk) 09:48, 27 May 2013 (UTC)

## Open and unbounded curves

Currently the lede says

Ellipses have many similarities with the other two forms of conic sections: the (open curve) parabolas and the (unbounded curve) hyperbolas.

This implies that parabolas are open but not unbounded, while hyperbolas are unbounded but not open. But it seems to me that both are open and both are unbounded -- if so, I think this needs to be reworded. Duoduoduo (talk) 21:09, 19 July 2013 (UTC)

I edited that sentence from what it was previously just today. The difference between unbounded and open did not make sense to me. I was merely trying to keep what seemed to be there already. My thought process was that maybe mathematicians made a distinction between the two. I would hate to think that I introduced an error by misinterpreting what was previously there. Perhaps it would help if someone can look at what was there before I edited it. TStein (talk) 05:39, 20 July 2013 (UTC)

## Simple proof of the area formula

Duoduoduo: My proof that you just reverted was probably much more useful that the one that you replaced it by, since it used a "known" result (the area of a circle) and a simple geometric argument that anyone who's mathematically inclined could follow. Jacobians and integration seem like complete overkill. However, I don't care enough to press the case. cffk (talk) 21:11, 21 July 2013 (UTC)

The "unproven" and "intuitive" result is proved as follows: the area $A$ is given by the integral

\begin{align} A &= \int_{-a}^a 2b\sqrt{1-x^2/a^2}\,dx\\ &= \frac ba \int_{-a}^a 2\sqrt{a^2-x^2}\,dx. \end{align}

The second integral is just the area of a circle of radius $a$, i.e., $\pi a^2$; thus we have $A = \pi ab$. In my book, this proof is so straight-forward that it doesn't need to be spelled out (and certainly the ancient Greeks found these results without resorting to calculus). cffk (talk) 00:11, 22 July 2013 (UTC)

## Uncited and dubious approximation formula

I have marked an uncited approximation formula as dubious. The article claimed it was 'better' but some simple comparisons with (1) Gnuplot's numerical elliptic integral routines, and (2) the Ramanujan approximation formula given in the article showed that the Ramanujan formula was always a better choice. I tested with a and b close to 1, close to 100, and various relative magnitudes of |a/b|.

It is possible that my little tests were somehow biased. I am not in a position to become more familiar with the various approximation schemes and cannot suggest a better formula. Frankly, the Ramanujan formula was a very good approximation. — Preceding unsigned comment added by 69.172.168.8 (talk) 04:04, 31 July 2014 (UTC)

I added back the 2nd Ramanujan approximation as someone compared it with his first in the Circumference article and the results were noticeably better as b got smaller (the other equation for a "special case" is another story-I don't know what the purpose of that was!).2001:4BA0:FFF4:10B:0:0:0:2 (talk) 18:09, 15 September 2014 (UTC)
Fair enough. But the way to make this "stick" is to include the reference to Ramanujan together with his error estimates. I've now added these. cffk (talk) 18:57, 15 September 2014 (UTC)