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Numerical and linear eccentricity[edit]

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[edit]

Parametric form in canonical position, missing angles in drawing[edit]

I agree with the archived comment requesting labels on the diagramme —DIV ( (talk) 06:54, 12 May 2013 (UTC))

Accuracy of formula[edit]

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 ( (talk) 06:55, 12 May 2013 (UTC))


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[edit]

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[edit]

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

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

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)