Talk:Maxima and minima

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[edit] Request for a figure with a 3-dimensional local maximum in this article

Such a figure would be of great heuristic value in generalizing visually the notion of maxima and minima. Perhaps it could be borrowed or adapted from the Saddle point article. Thanks. Thomasmeeks 13:12, 4 January 2007 (UTC)

I think you should post this request at Wikipedia:Requested images in the math section. There it will be more likely to be found. Oleg Alexandrov (talk) 16:40, 4 January 2007 (UTC)

OK, will do. Thx. BW,Thomasmeeks

May I help? I've generated a simple minimum point of a paraboloid with a tangent plane. Try: this image. I'm a new user, so if there's any problems, tell me on my user page. --Freiddy 11:38, 8 January 2007 (UTC)

That's actually a local maximum, not minimum. I think the picture looks good. Feel free to add it in. Oleg Alexandrov (talk) 15:57, 8 January 2007 (UTC)

Sorry, it's "Maximum". Typo. —The preceding unsigned comment was added by Freiddy (talk • contribs) 16:13, 8 January 2007 (UTC).

I made another version according to your suggestions. The image is image. Note: the extension is no longer in caps. The image is not quantitatively accurate since I didn't use a 3D program to draw the box, but it should explain the basic qualitative concept.--Freiddy 17:13, 8 January 2007 (UTC)

If you haven't noticed on my user talk page, I've already uploaded the two pictures you requested. They are Image:Maximum_tangentplane_boxed.png (just for now, please use the Image:Maximum_tangentplane_boxedN.png as a temporary substitute before this image is moved and replaces the other image) and Image:Maximum_boxed.png. The issues are dealt in my user page. --Freiddy 09:51, 12 January 2007 (UTC)

Alright, everything is okay now. Just use these two images (both 100% ready): Image:Maximum_boxed.png and Image:Maximum_tangentplane_boxed.png (problem fixed now). --Freiddy 17:08, 12 January 2007 (UTC)

Looks good like a thumb (see right). Nice. Feel free to add it (them) in. Oleg Alexandrov (talk) 17:27, 12 January 2007 (UTC)

Thank you so much, Freiddy. -- Thomasmeeks 18:33, 12 January 2007 (UTC)

If you want me to make the dot a little bigger, I can do it now. --Freiddy 12:43, 13 January 2007 (UTC)

I also corrected a few spelling errors and improved the structure of the section on Maxima_and_minima#Functions_of_more_variables. Is it necessary to include a few examples in this section? --Freiddy 12:55, 13 January 2007 (UTC)

Probably helpful. Yes, a bigger max bull's eye (and possibly fading the colors to bring out the max). My thx. Thomasmeeks 21:24, 13 January 2007 (UTC)

I'll do that, but what do you mean "fading the colors to bring out the max[imum]"? --Freiddy 09:32, 19 January 2007 (UTC)

Well, my thought was that if the blue-to-green faded more from the x-y axes approaching the max, it would be easier to pick up the red at the max. Alternately, instead of the reddish glow above the z values, possibly it could on the z values as it approached the solid red of the max with a black dot in the center.

On another matter, I had thought that lengthening the z axis so that the z label would not be in the web of the figure would be a good idea, but I see that to avoid obstructing the max the entire figure wouuld have to be rotated. And rotation would be a lot of work. So, that's probably out.

I also have 2nd thoughts about the 'cherry' reference in the article ('top' might be better), which I think would annoy mathematicians. I'm not happy about writing all this now rather than say I couple of weeks ago. Sorry.

I'd say best to hear from Oleg before doing anything. Or just leave as is. Its way good enough. My thx for your signal contributions. --Thomasmeeks 13:25, 19 January 2007 (UTC)

Well, I could do part of that. But then I'll have to start from scratch entirely (I'm quite busy these days). Also, I don't my graphing calculator has the capabilities. I hope you're not disappointed. But I could help you work on the text. --Freiddy 11:56, 26 January 2007 (UTC)

It was quite generous of to have made those figures, which are very good. They add another dimension to tha article. The best there is is, well, still the best. --Thomasmeeks 13:48, 26 January 2007 (UTC)

[edit] what are strict maxima and minima?

In some text, it says "strict local maximum", such as in http://stat-www.berkeley.edu/~peres/bmall.pdf, or the sentence "the origian can not be a proper local maximum" in http://www.springerlink.com/index/Q6164625N34P44Q3.pdf. Does it mean "strict local" or "strict maximum"?

In this article http://www.emis.de/journals/EJP-ECP/EcpVol5/paper11.pdf, it also says "strict fine maximum". does it mean "strict fine" or "strict maximum"?