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December 23

Circumcircles revisited

In the previous problem "Circumcircles of two triangles with a common edge", it struck me that the solution given misses the point in that it's really a problem in topology. Here is a more general version:

Given four distinct points P1, P2, P3, P4, and two Jordan curves A and B so that

A and B intersect in points P2 and P3 and in no other points, i.e. A∩B={P2, P3}.
A and B cross at these points, so there is a point of A-{P2, P3} inside B and a point of A-{P2, P3} outside B (and vice versa).
P1 is on A and P1, P2, P3 occur in order when A is followed counterclockwise.
P4 is on B and P2, P4, P3 occur in order when B is followed counterclockwise.

Then either P1 is inside B and P4 is inside A, or P1 is outside B and P4 is outside A.

I don't know how you would go about proving this statement though, no idea how to deal with the counterclockwise conditions. --RDBury (talk) 12:52, 23 December 2014 (UTC)[reply]

Is this how limits can work?

[Moved from Misc Desk]

Let a equal the number of people that are willing to see The Interview. Let b equal number of people unwilling to see The Interview. Let n equal the effect of publicity. Also, your x, y, and z stay the same [Let x equal the number of theaters in America. Let y equal the number of targets terrorists are capable of targeting simultaneously. Let z equal the number of theaters to not show the movie out of fear of attack.]

lim n -> ∞ [x - z] = a + b, and y has no place in the equation — Preceding unsigned comment added by 166.137.139.119 (talk) 20:44, 23 December 2014 (UTC)[reply]

Is this a question?

The following discussion has been closed. Please do not modify it.

I removed a template that said this isn't a question. There happens to be a very bold question as the title of this section. — Preceding unsigned comment added by 70.122.245.95 (talk) 19:57, December 23, 2014‎

Given the text of the question I seriously doubt it is a sincere one. If it is sincere, perhaps you could find a better/less trollish example. Please don't remove the hat again; bring it up at the Talk page if you want to discuss this removal further. - Eron^Talk 00:04, 24 December 2014 (UTC)[reply]

I have done so. May I suggest you take a look at Wikipedia:Assume Good Faith and then immediately look at Humility. — Preceding unsigned comment added by 70.122.245.95 (talk) 00:22, 24 December 2014 (UTC)[reply]

Hatting discussed at WT:RD#Now I'm a troll. -- ToE 11:48, 24 December 2014 (UTC)[reply]

Substituting more descriptive variable names:

e_p = effect of publicity

T_t = total number of theaters

T_u = number of unwilling theaters

P_w = population willing to watch the film

P_u = population unwilling to watch the film

You get:

\lim _{e_{p}\to \infty }T_{t}-T_{u}=P_{w}+P_{u}

Setting aside any conjecture concerning what infinite publicity effect even means, I don't think you intended to suggest that the total number of theaters outnumbered the total population. Perhaps you should rephrase your question. -- ToE 01:56, 24 December 2014 (UTC)[reply]

To be clear, this has nothing to do with limits. I don't understand your variables; I assume actually they're functions of publicity; but in any case, it should be obvious that "y has no place in the equation" because nobody, neither theater nor public, knows how many theaters the terrorists can target. There's simply nothing that is a function of y here. Wnt (talk) 04:37, 24 December 2014 (UTC)[reply]

You're probably right. You see, in high school after we learned matrices we learned the volume of cones and after that, there was no connection to real life. I remember solving limits and learning about functions, but I've no idea how to use them. If it is a function, what function is it. If my limit is not notated sensically, how should it be worded? — Preceding unsigned comment added by 70.122.245.95 (talk) 11:22, 24 December 2014 (UTC)[reply]

I believe that you are asking how to express in a formula that the number of people willing to see the movie may be a function of the publicity and of the number of theaters willing or unwilling to show it, but that it is not a function of the number of targets terrorists are capable of targeting simultaneously. I think that it really is easier to express in words, but if you have a multivariate function f(w,x,y,z), one way of saying that f really is not a function of y (that is, that f does not change as y changes as long as the other variables are held constant) is via partial derivatives:

{\frac {\partial }{\partial y}}f(w,x,y,z)=0.

-- ToE 12:43, 24 December 2014 (UTC)[reply]