The Four Colour Theorem

The four colour theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colours are required to colour the regions of the map so that no two adjacent regions have the same colour.

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This video was made in association with The Math Centre at Humber College, by Thomas Fraser.
Producer - Cameron Redsell-Montgomerie

[ScienceallOrg]

Great video! Did you really mean "simply connected" rather than "connected"? I've seen that wikipedia says so (and I assume you did too), but I've always thought that the connectedness of countries sufficed...

[juliobardem]

this is just like playing minesweeper, to each color assign a number, example: red = 1, blue = 2 ... consecutively up to 4, now don't join the even numbers. That's it.

[michaelbauers]

clear introduction to map coloring.  Yet another in the major theorem proved in my lifetime theorems.  Fermat's, 4 color, Poincare Conjecture...solved.  Is twin prime close?  Reimann Hypothesis seems to be one that might not fall in my lifetime

[TiKayStyle]

I read in Wikipedia everything about it. Sphere, Torus, Klein Bottle.
And in 3D the number of colors can be infinity.
BUT
What, if we ask for the number of colors in n-dimensions, where the "room" is divided by n-dimensional cubes?
2D Square
3D Cube
4D Hypercube
...

[TubeFish]

How do you set up the camera etc. to get such good light levels? Your hand doesn't seem to cast a shadow.

[Randomness]

I know this because of a 2008 Japanese movie, called 'Suspect X' such a great movie, I recommend it, thank me later 😉

[lordsiomai]

i wish my teacher taught this as clear as this. Nice video man thanks!

[Remanx]

who all ended here seeking help for:Ways to color a 3xN Board problem

[LaytonMathieson]

I made a map that defies the 4 colour theorem

[seanwells]

Reborder to hexagons, prove color by only 3 colors. Go home.