Absurdism
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| Joined: 18 Jul 2013 |
| Total Posts: 2568 |
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| 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
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| Joined: 18 Jul 2013 |
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| 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
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| Joined: 14 Aug 2008 |
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| 18 Oct 2013 04:51 PM |
| what the hell is a KAdCraS |
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Absurdism
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| Joined: 18 Jul 2013 |
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| 18 Oct 2013 04:52 PM |
| I ask myself that everyday. |
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Absurdism
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| Joined: 18 Jul 2013 |
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| 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
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| Joined: 29 Nov 2012 |
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| 18 Oct 2013 05:28 PM |
| oh wow, this is complicated |
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Absurdism
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| Joined: 18 Jul 2013 |
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| 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
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| Joined: 14 Aug 2008 |
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| 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
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| 18 Oct 2013 05:57 PM |
i dot imgur dot com slash KAdCraS png
lrn2figureoutobscurepatternsofcharacters |
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Absurdism
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| Joined: 18 Jul 2013 |
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| 18 Oct 2013 06:29 PM |
| Okay, but what IS a kadcras? |
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Absurdism
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| 18 Oct 2013 06:37 PM |
| "I ask myself that everyday." |
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| 18 Oct 2013 06:40 PM |
| Okay, but what IS a kadcras? |
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cntkillme
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| Joined: 07 Apr 2008 |
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Absurdism
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| Joined: 18 Jul 2013 |
| Total Posts: 2568 |
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| 18 Oct 2013 06:43 PM |
| Okay, but what IS a Sarcdak? |
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| 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
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blocco
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| Joined: 14 Aug 2008 |
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| 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
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| Joined: 22 Dec 2010 |
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| 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
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| Joined: 18 Jul 2013 |
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| 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
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| Joined: 14 Aug 2008 |
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| 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
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| Joined: 18 Jul 2013 |
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| 18 Oct 2013 07:00 PM |
| i give a hoot i just don't talk to you |
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blocco
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| Joined: 14 Aug 2008 |
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Absurdism
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| Joined: 18 Jul 2013 |
| Total Posts: 2568 |
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| 18 Oct 2013 07:05 PM |
| No, that is a remark on my shyness. |
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