User talk:Bernard Gottschalk

ELLIPSE

Greetings from Canada, and WELCOME to Wikipedia!

Sorry for the confusion about the Ellipse article. Sorry also for the lack of documentation about Wikipedia and editing it—I also had to learn as I went. Fortunately, sometimes we do encounter some helpful Wikipedians! I’ll attempt to be one myself with you.

So, you had changed the Ellipse article. Here are your edits:

Section: METRIC PROPERTIES You had added the part in bold here: All metric properties given below refer to an ellipse with equation $$\frac{x^2}{a^2}+\frac{y^2}{b^2}= 1 $$, except for $$A_\text{ellipse}$$ of a tilted ellipse.

Section: AREA You had added this whole new text at the end of this section: So far we have dealt with erect ellipses, whose major and minor axes are parallel to the $$x$$ and $$y$$ axes. However, some applications require tilted ellipses (see figure). In charged-particle beam optics, for instance, the enclosed area of an erect or tilted ellipse is an important property of the beam, its emittance. In this case a simple formula still applies, namely: $$A_\text{ellipse} = \pi\; y_\text{int}\, x_\text{max} = \pi\; x_\text{int}\, y_\text{max}$$ where $$y_{int}$$, $$x_{int}$$ are intercepts and $$x_{max}$$, $$y_{max}$$ are maximum values. This reduces to $$\pi\,a\,b$$ in the special case of an erect ellipse. For a proof, with applications to beam line design, see (reference).

I have undone my own revision and reverted the article back to how it was after you changed it.

Cheers!

CielProfond (talk) 22:43, 1 February 2021 (UTC)