Arpan Dutta what if you have a square divided into four like above (two colours), then surround it with another box. Split that box into three so that one rectangle touches the side of the bottom right box (covers the bottom side completely) and touches the bottom left box (covering half of the bottom side), and next box does the same covering the bottom right box (covering all the right side) and half of the top right box. Those two sub divisions will touch each other at the bottom right corner, the remainder of the box will snake around the other side of the original box touching the other sides of those two other boxes making up the rectangle. I can’t colour this with fewer than five.
@@Amaglabiddiaghloughbuite Alex, you can't disprove a valid proof :D(it is a theorem meaning that it does have a proof) so you must have missed a valid colouring
@@revengeofthenoobs1579 yeah I found a solution, but it was fun though. i bet you could make a great newspaper puzzle where you have to find the solution to complex shapes
@@janPeja "Poland" (green, top) is shown touching two red regions, which it doesn't do on the map. The homeomorphism is right, but he's made a slightly different colouring. Edit: actually, Poland seems to have an extra neighbour. It looks like he split a region to make the black/blue pair at some point when he was colouring. That's my guess, anyway. Edit²: the thumbnail (see also 3:05) shows only 8 regions on the right, whereas the map on the left has nine countries, so he "fixed" it while colouring.
DIVYA RAGHAVAN yes but not explainable with paper, way too long (I think you need to proof like 4500 cases...) as of now there is only computer that can show it. The 5 colors theorem can be proved quite easily though (same idea, just with 5 colors)
susmita mohapatra a ton of proofs has been published but all had errors... if you find a true proof of it you won a million dollars. If it’s that simple I don’t think it’s good...
oh god your way of teaching is energetic and interesting....
Wow I want teachers like him in my university ❤️
Hi there! What level are your students in?
Thanks Sir, Great Explanation
Great👏👍
What about 4 joined squares in a circle?! Still do with 4 colours?
The squares on oposite coners can have same colour( since the dont have a common edge between them ) so the chromatic number is 3. Hope this helps.
Arpan Dutta what if you have a square divided into four like above (two colours), then surround it with another box. Split that box into three so that one rectangle touches the side of the bottom right box (covers the bottom side completely) and touches the bottom left box (covering half of the bottom side), and next box does the same covering the bottom right box (covering all the right side) and half of the top right box. Those two sub divisions will touch each other at the bottom right corner, the remainder of the box will snake around the other side of the original box touching the other sides of those two other boxes making up the rectangle. I can’t colour this with fewer than five.
@@Amaglabiddiaghloughbuite Alex, you can't disprove a valid proof :D(it is a theorem meaning that it does have a proof) so you must have missed a valid colouring
@@revengeofthenoobs1579 yeah I found a solution, but it was fun though. i bet you could make a great newspaper puzzle where you have to find the solution to complex shapes
I think that the "simplified" map is wrong, with germany not touching the check republic.
it's flipped like in a mirror. still homeomorphic
@@janPeja thank you
@@janPeja "Poland" (green, top) is shown touching two red regions, which it doesn't do on the map. The homeomorphism is right, but he's made a slightly different colouring.
Edit: actually, Poland seems to have an extra neighbour. It looks like he split a region to make the black/blue pair at some point when he was colouring. That's my guess, anyway.
Edit²: the thumbnail (see also 3:05) shows only 8 regions on the right, whereas the map on the left has nine countries, so he "fixed" it while colouring.
Do four color theorem has a proof?
DIVYA RAGHAVAN yes but not explainable with paper, way too long (I think you need to proof like 4500 cases...) as of now there is only computer that can show it. The 5 colors theorem can be proved quite easily though (same idea, just with 5 colors)
@@thierryleclaire2636 Well, I just figured out a proof for it on paper. It's a really short intuitive proof. I am looking to publish it.
susmita mohapatra a ton of proofs has been published but all had errors... if you find a true proof of it you won a million dollars. If it’s that simple I don’t think it’s good...
You don't win a million. It's not one of the seven millennium prize problems.
@@susmitamohapatra9293 I think that this is false. Give us a link to the "proof" please.
What color will you choose for this new state I drew with no color as in the pic here - photos.app.goo.gl/hhpJ1Zuy8tawzAKZA
U can the states in the opposite will can have same colours
@@EpicGlitchyJuice but it is still touching
@@mune4522 bruh but its allowed
@@EpicGlitchyJuice he didn't say that. He said that if it touches it can't be the same color
@@mune4522 he says points don't count, only borders. so those corners don't count as touching.