DRAW A MAP BY FOUR COLOURS (am i solve it ?)

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tarek like math
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DRAW A MAP BY FOUR COLOURS (am i solve it ?)

Unread post by tarek like math » Sun Apr 17, 2011 2:05 am

IS MY SOLUTION OF DRAW A MAP BY FOUR COLOURS IS RIGHT !!
[I am not sure that i solve this problem but i want to sure about it so i publish it on forum, please everyone help me to be sure about its rightness] :

imagine a circle named Desh coloured by C1. infinite points it can contain but no
matter u can seperate them by two colours u should coloured all bijore points
as c2 and all jure colour as c3. if contained all points are bijore then u
can find c2 colour at first and again c2 colour at end both mathing in same
place in the end of circle. so u can't use c2 colour at end because if u do
so there will be two point as same colour so u should seperate last point by
use c4.
by use this way u can separately colour Desh and all his neighbouring country,
just imagine neighbouring countries as poridistho points. easily u can
seperate them by use only four colour.
now imagine a specific neighbouring country is Desh2 and think it is a
circle. now problem is how u can seperate neighbouring countries of Desh2
and Desh2 itself.suppose Desh2 is member of c2. naturally it is neighbour
of colour c1 & c3. u can suppose Desh2 circle has infinite points in its
poridhi. now it's coloured by c2 and 3 of its poridhisto points which are
neighbour of each other coloured as c3,c1,c3. so this how u can seperate
all of its poridhistho points. u can colour all bijore by c1 and all jore
by c3 and as like as Desh1 circle if contained points are bijore u can
seperate all points by use c4 to colour last point.
in special case if Desh2 share a point which coloured by c4 then how u can
manage it by only four colours ? then Desh2 has 3 points in its poridhi
which are neighbour of each other coloured in 3 different colours example
c3,c1,c4 and it itself coloured by c2. in this case u can ignore carefully
one colour like c1 or c3 or c4 and colour all its poridistho points by other
two colours.
this how u can circling all Desh by cosidering them as circle. by base on
this method u can also solve problem of new born country.
these are the main ways two solve this historical problem but need to exam
by a mathematician. it is so important to justify by a mathematician.
please help all reader ?

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Moon
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Re: DRAW A MAP BY FOUR COLOURS (am i solve it ?)

Unread post by Moon » Tue Apr 19, 2011 11:46 pm

Sorry for replying late. First of all, I don't understand many parts of your proof. So here are my questions:
1. What are 'bijore' and 'jure' point? If you mean odd and even by them, how can we define some point as odd or even?
2. Another problem is that I don't really understand how you can assume a country to be circle. The countries can be of many different shapes (Desh 1 can have common points with every other countries). I don't think that your proof will work in that case.

OK the one advice I can give you is to write the solution in Bangla (either in Bangla letter or english letters), define everything clearly and submit again.
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Zzzz
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Re: DRAW A MAP BY FOUR COLOURS (am i solve it ?)

Unread post by Zzzz » Tue Apr 19, 2011 11:58 pm

I also haven't understand some parts. Here is my first question:

Probably you meant something like this in the second para of your proof:
desh.JPG
desh.JPG (5.37KiB)Viewed 3229 times
Then what should I do if first and third neighboring country have same border? You said alternatively we will colour the first point with C2, second with C3, third with C2 and so on. Well, first and third point on circumference (poridhi) of a circle don't have anything common. But when you are considering those as countries, surely they can have a common border.
Every logical solution to a problem has its own beauty.
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tarek like math
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Re: DRAW A MAP BY FOUR COLOURS (am i solve it ?)

Unread post by tarek like math » Wed Apr 20, 2011 10:22 pm

let i define two country as d1 and d2. if they have some common neighbouring country then they can be colour by only c3 and c4 because c1 and c2 are d1 and d2's own colour[there d1,d2 neighbour of each other ].if d1 not neighbour of d2 then they both can colour by c1 and their common n. c. can colour by c2,c3,c4. it is a common thing then other.
suppose d1 & d2 have some common n.c. as a,b,c,d...member of d3 group. now "a" has a border with both d1 & d2. suppose a share some part of border of d1 which colour by c2 then solution is "a" should colour by c4. think b other d3 country next to a in d2's border.b share border of d1 which part of d1's border is colour by c2 and two c3 in it's both side means c3,c2,c3 pattern. now solution of colour of b is below. b can't be colour by c4 because "a" colour by c4 and b next of a. then b should be colour by c3. and so where b share border of d1 should re-colour by c3 and it's both side which colour by c3 should re-colour by c4. this how no same colour can be repeat in boundary of d1.
i think it's no matter to d1's border if some colour4 comes in it's boundary.
my solution can be wrong but i write a lot more about it in my home use many pages but i think more problem should be faced more picture i should give. but i think it still has some chance. dear repliers please carry on.

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