Wikipedia:Reference desk/Archives/Mathematics/2010 May 25

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May 25

Sophocles' Antigone

I've been reading the Seamus Heaney translation of Antigone. I'd like to ask as to the point of Antigone reburying Polyneices. Is this a plot device or was there something else at work here. I've heard that in tradition the once pouring of soil over the body was enough to commute the soul to Hades? —Preceding unsigned comment added by 86.177.175.194 (talk) 00:08, 25 May 2010 (UTC)

I think you might be better off at the Humanities reference desk for that one. Qwfp (talk)

algebra manipulation

Resolved

I need to change this:

$t={\frac {2{\sqrt {\left({\frac {1}{2}}vt\right)^{2}+L^{2}}}}{c}}$

into this:

$t={\frac {2L/c}{\sqrt {1-v^{2}/c^{2}}}}$

How do you do it?--Wikinv (talk) 07:45, 25 May 2010 (UTC)

Using simple algebra? Multiply both sides by c, square both sides, gather all the resulting t^2 terms to the LHS, divide by the co-efficient of the t^2 term, divide the RHS numerator and denominator by c^2, take the square root. Q.E.D. (Marking this as resolved, any more help would basically be doing your homework for you.) Zunaid 08:03, 25 May 2010 (UTC)

A derivative of sorts?

Suppose ƒ is a continuous function of infinitely many real variables, and that 0 is an "identity element" for ƒ in the sense that

$f(0,\alpha ,\beta ,\gamma ,\dots )=f(\alpha ,\beta ,\gamma ,\dots ).\,$

Has anyone thought about the following limit (in particular, is there anything in the literature on it)?

$\lim _{\Delta \alpha \to 0}{\frac {f(\Delta \alpha ,\ \alpha ,\ \beta ,\ \gamma ,\dots )-f(\alpha +\Delta \alpha ,\ \beta ,\ \gamma ,\ \dots )}{\Delta \alpha }}$

In case it makes anyone feel any better, for my purposes it may suffice to assume all but finitely many of the variable are zero (but of course with no prior finite bound on how many nonzero ones there are). Michael Hardy (talk) 19:31, 25 May 2010 (UTC)

....and now I have what for my present purposes is a sufficient answer to this, via Math Overflow. Michael Hardy (talk) 17:04, 26 May 2010 (UTC)

Perimeter estimation

What is the use of knowing the total arc length,on positive Cartesian, of an astroid expressed by (x/a)^r+(y/b)^r=1? May it be just an artistic-math? Why the term "elliptic integrals of second kind"? Is it only to evaluate the arc length of the above astroid when r=2,the ellipse? Why the perimeter of an ellipse so important? Is it due to "planet's orbit shape"? Are the shapes elliptical?TASDELEN (talk) 21:47, 25 May 2010 (UTC)

Yes, planetary orbits are elliptical, see Kepler's laws. Arc length has all kinds of applications, and superellipses (I never heard the term "astroid") with r=2.5 or so are a nice shape that has been used in architecture. 69.228.170.24 (talk) 14:35, 26 May 2010 (UTC)

Here's a link in case there's more than one person on earth who's never heard the term: astroid. Michael Hardy (talk) 17:07, 26 May 2010 (UTC)

• OK for the term "astroid". Then, how to name the shape of the expression (x/a)^r+(y/b)^r=1 ? We know: for r=1 the name is a "line"; for r=2 the name is an "ellipse"; for r=2/3 the name is what we call a real astroid; for r=0,397 what should be name?

Why Kepler (1609), Euler (1773), Muir (1883),...Ramanujan (1914),....were so much interested only by the perimeter of an ellipse? Was it due to Kepler's orbital laws? Or their interest was only about geometric solid shaped ellipse: a closed, plane shape, while the physical orbits may be different from being elliptical, as Newton's F*r*dt=m*r*dv (total energy equation) may proove?TASDELEN (talk) 18:29, 26 May 2010 (UTC)

Apollonius of Perga studied the ellipse, but not the other astroids. The arc length of the circle was computed by Archimedes. The problem of the arc length of the ellipse was unsolved for a long time. The motivation for attacking such problems was probably mathematical challenge rather than commercial value of the result. Bo Jacoby (talk) 12:29, 27 May 2010 (UTC).

• So,you name the expression (x/a)^r+(y/b)^r=1 as astroid.OK.I am looking for an expansion of the total arc length of these astroids on positive Cartesian.Some thing similar to MacLaurin's expansion series for ellipse.Any help? TASDELEN (talk) 18:23, 27 May 2010 (UTC)

no, you defined the astroid. I did not know that word before. Bo Jacoby (talk) 10:57, 28 May 2010 (UTC).

• Any series expansion known? For example for r=2, the ellipse, we have McLaurin's perfect series expansion. TASDELEN (talk) 18:55, 28 May 2010 (UTC)

Equivalency

Do you know a power expression which is the equivalent of the elliptic integrals of second kind?TASDELEN (talk) 22:05, 25 May 2010 (UTC)

? There appears to be one at Elliptic_integral#Complete_elliptic_integral_of_the_second_kind - you meant power series or something else?77.86.125.207 (talk) 03:39, 26 May 2010 (UTC)

• I meant a power series for (x/a)^r+(y/b)^r=1.A MacLaurin's similar series as stated in Elliptic_integral#Complete_elliptic_integral_of_the_second_kind when r=2. When (r) is not equal to (2) the eccentricity (k) has no sense. For example when r=3, are there series expansions? Or something similar? TASDELEN (talk) 07:28, 26 May 2010 (UTC)