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Re: an interesting problem

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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 04:42 PM
In making something silly as a demonstration for the applications of arctangent, I happened upon an interesting bump. Consider the following image: KAdCraS
Two blocks are placed collinearly. Let us define one moving part as A (marked with diagonal lines), and the other with B (solid). A will move in order to get away from B, which constantly chases the other. There are eight such predefined vectors indicating 1- or 2-stud movement. If A or B will move outside of the X by X bound in order to get closer or farther away, they are forced to pick another direction.
As opposed to taking a simple route, I thought it might suffice to try to make a greedy algorithm that forces A(x, y) to travel to some point, creating a maximal distance between B(a, b). Beginning with the generic distance formula as a function of x, y, a and b:

s(x, y, a, b) = ((x-a)^2+(y-b)^2)^.5

Take the partial derivative with respect to x:
δs/δx = (x-a)/((x-a)^2+(y-b)^2)^.5

Search for a global maxima:
(x-a)/((x-a)^2+(y-b)^2)^.5 = 0

It doesn't matter how I go about it, there is always an extraneous solution to this problem. x must always equal a. That's the logical answer. Algebraically, we can only obtain that x = y and a, b are nonzero. Also, a - b is nonzero. Why does the derivative state that the most distance occurs when the points are at a = x for some b and y (A(a, y), B(a, b))? We can state at the beginning that, in order to get the most distance, A would tend toward a corner in the bound.
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 04:45 PM
"Algebraically, we can only obtain that x = y and a, b are nonzero. Also, a - b is nonzero."
I meant to say: Algebraically, we can only obtain that x = a and b, y are nonzero. Also, y - b is nonzero.
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blocco is not online. blocco
Joined: 14 Aug 2008
Total Posts: 29474
18 Oct 2013 04:51 PM
what the hell is a KAdCraS
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 04:52 PM
I ask myself that everyday.
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 05:26 PM
OK, so perhaps it has something to do with the answer being infinite. It's not a bounded derivative. How do we bind the partial derivative to the interval [X, X]?
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uyjulian is not online. uyjulian
Joined: 29 Nov 2012
Total Posts: 1214
18 Oct 2013 05:28 PM
oh wow, this is complicated
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 05:29 PM
Not really. All we're doing is trying to solve for x and y properly.
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blocco is not online. blocco
Joined: 14 Aug 2008
Total Posts: 29474
18 Oct 2013 05:34 PM
Had I seen the image KAdCraS I would be able to figure it out.
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 05:34 PM
It's imgur, blocco.
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DrAgonmoray is not online. DrAgonmoray
Joined: 29 Jul 2008
Total Posts: 17428
18 Oct 2013 05:57 PM
i dot imgur dot com slash KAdCraS png


lrn2figureoutobscurepatternsofcharacters
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 06:23 PM
^
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ArceusInator is not online. ArceusInator
Joined: 10 Oct 2009
Total Posts: 30553
18 Oct 2013 06:29 PM
Okay, but what IS a kadcras?
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 06:37 PM
"I ask myself that everyday."
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ArceusInator is not online. ArceusInator
Joined: 10 Oct 2009
Total Posts: 30553
18 Oct 2013 06:40 PM
Okay, but what IS a kadcras?
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cntkillme is not online. cntkillme
Joined: 07 Apr 2008
Total Posts: 44956
18 Oct 2013 06:42 PM
It's obviously a Sarcdak
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 06:43 PM
Okay, but what IS a Sarcdak?
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ArceusInator is not online. ArceusInator
Joined: 10 Oct 2009
Total Posts: 30553
18 Oct 2013 06:46 PM
Legends tell of two dragons that lived long ago, Kadcras and Sarcdak. Kadcras was mad so he said

"sarcdak get ovr here"

"wat"

"sarcdak u r bad"

"no"

"whyyyyyyyy"

the end
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cntkillme is not online. cntkillme
Joined: 07 Apr 2008
Total Posts: 44956
18 Oct 2013 06:47 PM
dark sac
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blocco is not online. blocco
Joined: 14 Aug 2008
Total Posts: 29474
18 Oct 2013 06:48 PM
teachers are chefs
they give us food to eat
then we get graded on how well we ate it

yeah i went deep in metaphor so wut
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dekkonot is not online. dekkonot
Joined: 22 Dec 2010
Total Posts: 6685
18 Oct 2013 06:50 PM
I feel as though that story, Arceus, needs to be written down for future generations.

~ Linguam latinam est optimum ~
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 06:54 PM
It already has been, dekkonot.
This just goes to show that every time I make a legitimate mathematics thread, it goes down in history because someone says something amazing yet off topic.
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blocco is not online. blocco
Joined: 14 Aug 2008
Total Posts: 29474
18 Oct 2013 06:57 PM
yet when i say off topic things that are profound no one gives a hoot
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 07:00 PM
i give a hoot i just don't talk to you
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blocco is not online. blocco
Joined: 14 Aug 2008
Total Posts: 29474
18 Oct 2013 07:04 PM
is that an insult
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Absurdism is not online. Absurdism
Joined: 18 Jul 2013
Total Posts: 2568
18 Oct 2013 07:05 PM
No, that is a remark on my shyness.
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