Talk:Coordinates (elementary mathematics)

Moving this from the article page to here:

FURTHER WORK REQUIRED

• theta=arctan(y/x) need a fix to make values in the adequate range.
• Some conversion matrices of derivatives need fact-checks.
• Simple figures would be a great help.
• Should we mention that Cartesian really means the oblique coordinates?

RickK 04:22, 18 Jan 2004 (UTC)

• Linked an existing figure for cartesian coordinates.
• Made a new one for circular coordinates. Tell me if I should change something.
• Switched two lines in the last matrix in the cartesian-spherical section. Could someone doublecheck?

DrZ 22:05, 20 Feb 2004 (UTC)

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Let theta= the degree of angle arctan= the inverse tangent y = the value on the y-axis x = the value on the x-axis

Therefore, Theta = arctan (y/x)

(y/x) is tangent function, so the angle is figured out by inversing it.

(literally r is the hyptoneus of the triangle.) 03:19, 8 Apr 2005 (UTC)

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I have changed all radian angles to degrees. While I prefer radians, too, I guess people not yet familiar with coordinate systems might have difficulties with them. Also, I'd have to change my pic otherwise :-) DrZ 22:05, 20 Feb 2004 (UTC)

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(My suggestion is my property; if you wanted to copy it, note that's it's me, 11 years old Harris Chan)

I have some suggestion to add on the conversion between the the polar coordinate and the circluar (may be someone thought of this already?): r= y / sin Ø = x / cos Ø.

And (thetha)= tan ^-1(y / x)= sin^-1; (y / r)= cos^-1 (x / r)

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Changes

Aren't the "polar coordinates" and "circular coordinates" listed here the same thing? It appears to be a holdover from when separate pages were merged. Also, what would people think of rearranging so that all the 2-D is in one major section, and the 3-D in another major section? --zandperl 23:51, 15 Apr 2004 (UTC)

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http://mathworld.wolfram.com/SphericalCoordinates.html gives quite different values for the derivative conversion matrices. It would be good to straighten this out. --Mmm 06:36, Apr 20, 2004 (UTC)

Could you specify which matrix you mean? I could only find one common matrix on both sites (the jacobian for the spherical - cartesian conversion), which seems to be essentially the same. DrZ 14:35, 28 Jun 2004 (UTC)

The spherical-cartesian matrices were the same, I agree. When checking it, though, the intermixing of "engineering" and "math" (different phi-theta convention) coordinates was extremely unhelpful, so I deleted the set inconsistent with the above article. Might want to bring back the vector relations in some form if it can be done without confusion, though. 11 Jul 2004

Mistake

In the chapter "Conversion between.." the vector of the drivates is calculated as the matrix-product of the Jacobian matrix and the vector of given derivates. Hence, you should use parenthesis instead of the lines denoting determinates (\pmatrix instead of \vmatrix). Refer also to "mathworld.wolfram.com", where brackets are used. This mistake was transfered to German wikipedia, where i am going to correct it. -- 81.210.158.250 13:36, 12 Feb 2005 (UTC)

This is now repaired. Problem - the links under "credit to original articles" in the "see also" section seem to be broken. Paul Reiser 18:21, 13 Feb 2005 (UTC)

Math vs. Physics Convention

Hi, I posted an item to the Wikiproject Math talk page, but I thought I should put a comment here too.

It seems that the convention used here is that common in mathematics, while most other pages, including most importantly perhaps Nabla in cylindrical and spherical coordinates, use the convention common in physics, whereby <math>r<math> is the length of the vector, and <math>\rho<math> is the length of the projection onto the <math>xy<math>-plane. I think that this should probably be the convention adopted here as well (at least those that have discussed so far at the wikiproject page seem to think so, and I'll yield to their judgement). So I'm changing all of the material at this page to match what is at the Nabla in coords page, and putting the result at user:jacobolus/coordinates temporarily. It will take a while, and I'll post back when I'm done. Anyway, it really seems to me that we benefit from consistency, with prominent disclaimers at the top (right now there are tiny notes tucked in the bottom of both pages). --jacobolus (t) 20:17, 6 Mar 2005 (UTC)