Wikipedia:Reference desk/Archives/Mathematics/2008 November 30

= November 30 =

Polar graph racism?
My friend says that polar graphs are "racist". Is that true, and if it is, why?

♫Deathgleaner 04:17, 30 November 2008 (UTC)


 * have you asked him why? There is nothing inherently race oriented in the definition of polar graphs.  Specific instances of polar graphs might be considered racist.  The closest example I can think of would be the placing of the prime meridian in Greenwich, London, although that is a Spherical coordinate system.  Taemyr (talk) 05:11, 30 November 2008 (UTC)


 * It sounds like a joke to me. Ask him for the punchline. StuRat (talk) 06:45, 30 November 2008 (UTC)


 * Presumably because they are based on Poles - that's as worthy of the word "joke" as the likelihood that Fermat had a solution to the Riemann hypothesis.→81.154.106.229 (talk) 09:42, 30 November 2008 (UTC)


 * I'm swinging both ways on this, are they really racist? If you're really worried how about just using bipolar coordinates? Dmcq (talk) 12:18, 30 November 2008 (UTC)


 * Did a manic-depressive invent those ? StuRat (talk) 17:50, 30 November 2008 (UTC)

I would have said that Cartesian graphs are more racists than polar ones. In Cartesian coords someone have arbitarially assigned the right side to positive numbers reinforcing the oppression of lefties who are seem as negatives! Further they seperate out the horizontal and vertical which is an afont to those with a diagonal inclination! --Salix (talk): 18:08, 30 November 2008 (UTC)
 * Clearly a revolutionary approach is needed. Algebraist 18:15, 30 November 2008 (UTC)


 * Those polar graphs should be shown the error of their ways. Apply an inversion and they'll see what happens to their circle of friends. Dmcq (talk) 20:04, 30 November 2008 (UTC)


 * This is my joke. Why Deathgleaner put this up is a mystery. Also, there's no punchline. onekopaka (talk) 00:35, 1 December 2008 (UTC)

It's possible that your friend has read some of the stuff that Arno Peters wrote. He was very much into reading political implications into the Mercator projection. It all seemed like a crock to me. Oh, I admit it's not impossible that people who lived in Europe and North America were influenced by the way the map made their homelands look bigger relative to equatorial zones. But Peters didn't do himself any favors with his obvious shallow understanding of the underlying mathematics.

Anyway if I recall he didn't like polar projections because they were usually centered at the North Pole, and (depending on the projection) tended to distort southern areas more than northern ones. --Trovatore (talk) 03:46, 1 December 2008 (UTC)

Limit
Hello,

I am stuck with this following limit $$\lim_{x\to\infty}\frac{\sqrt{x}}{\sqrt{x+\sqrt{x+\sqrt{x}}}}$$.

Rewriting into $$\lim_{x\to\infty}\frac{\frac{1}{\sqrt{x+\sqrt{x+\sqrt{x}}}}}{\frac{1}{\sqrt{x}}}$$ and using l'Hopital result in lengthy derivatives with no result. Anything I am missing?

Thanks --Gnorkel (talk) 20:43, 30 November 2008 (UTC)
 * Rewrite as $$\lim_{x\to\infty}\frac{1}{\sqrt{1+\sqrt{\frac{1}{x}+\frac{1}{x^{3/2}}}}}$$. Conscious (talk) 21:05, 30 November 2008 (UTC)
 * We're really not supposed to do people's homework for them (see top of page). In the future it would be better if you could find a way to point the person in the right direction, rather than doing everything but the last (trivial) step.
 * For Gnorkel: This is a good case to remember. Beginners have a strong tendency to overuse l'Hôpital's rule.  L'Hôpital is a good thing to have in your bag of tricks, but that's the way to think of it: a trick that sometimes helps, not the default approach to the problem, and never a substitute for understanding what's going on. --Trovatore (talk) 06:56, 1 December 2008 (UTC)

Third derivative
A point on a curve where the second derivative changes sign is known as an inflection point and is where the curve changes concavity. What would one call/describe a point on a curve where the third derivative changes sign? —Lowellian (reply) 22:14, 30 November 2008 (UTC)


 * I don't think maths has a term but jerk and yank might be interesting to you. They are very relevant to roller-coaster design. Dmcq (talk) 23:19, 30 November 2008 (UTC)
 * I see jerk also mentions snap crackle and pop :) Dmcq (talk) 23:24, 30 November 2008 (UTC)


 * If you have 2nd and 3rd derivatives both zero then you have an especially flat part of the curve. If just the 3rd is zero then a the curve will closely approximate a parabola at the point (technically the curve will have high Contact with a parabola). --Salix (talk): 23:53, 30 November 2008 (UTC)