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Anonymous
Four Quadrants Theorem 2016-11-04 23:21:13 Post No. 8455460
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Four Quadrants Theorem 2016-11-04 23:21:13 Post No. 8455460
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Can someone explain (or prove, though not required) why two intersecting perpendicular lines diagonally across a plane with an infinitely small circle of radius r in the center does not disprove the Four Color Theorem? In the middle do they all not touch and either two sections of the four quadrants would be forced to touch along the sides, or through the center, or standing as it is in pic related where the four quadrants support the Four color theorem, the circle that is colored any color would touch one of the four quadrants?
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Can you articulate in a little shorter sentences?
Also, state what you think the theorem is about.
Also
>infinitely small circle of radius r
while you shouldn't even fall for the Descartes meme of thinking it needs points to make up for lines and planes, please don't reason with infinitesimals like properties for finite things apply to them
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In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions.[1]
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>>8455460
The four color theorem states that THERE EXISTS a coloring of any map with only four colors such that no two colors are adjacent.
You already fucked up because you colored the map in such a way that it's impossible to color the fifth region. You need to find a different coloring.
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>>8455479
Fair enough, but I also thought that the picture was fairly explanatory.
The Theorem just states that on a plane any amount of regions drawn on that plane can be colored with four colors such that no touching regions have the same color.
As for the proof something something summing vertices and edges.
>while you shouldn't even fall for the Descartes meme of thinking
Good point
I wasn't saying that "hey this disproves the Four Color Theorem" I was simply asking the logic behind my conjecture being false.
>>8455484
Yes, I'm asking why the green and blue quadrants on opposite sides don't "touch" """through""" for lack of a better term circle of r->0
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>>8455460
>an infinitely small circle of radius r
that r is the diameter tho
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>>8455501
lol good point.
let r = diameter of the circle, fuqq it.
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>>8455500
>Yes, I'm asking why the green and blue quadrants on opposite sides don't "touch" """through""" for lack of a better term circle of r->0
Even if the circle weren't there, the opposite sides wouldn't touch. Corners don't count as touching.
From wikipedia:
>Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions.
https://en.wikipedia.org/wiki/Four_color_theorem
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>>8455509
>that is not a corner
Oh, hey thanks. Dare I ask what the proof would be like if corners were included?
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>>8455562
You could trivially make a map that requires arbitrarily many colors. Just take a circle and draw a bunch of diameters through the middle at different angles.
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An infinitesimally small circle is a point, which can be said to be the point where all 4 quadrants intersect
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