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How many colors are in this map? I have actually placed the clue in the question with colors. Yes, there are 4 colors. Yellow, red, blue and green. But that's not the only interesting feature of this map. No two neighboring countries are the same color. They would have merged then, right? This means that we need to use at least 4 colors in order to distinguish the countries of the world from each other. Now I will go further and make the following claim; We don't need more than four colors. No more than four colors are needed to color the world. I will go even further now and say: You don’t need more than four colors to color not just the world, but any map. Only four colors are enough, no matter what map you color as long as it is planar. By using 4 colors alone, you can ensure that adjacent regions are not the same color. It does not necessarily have to be a map of the world and the countries on it, as it is here. It can also be continents or the states of the United States of America, choose any 4 colors and start painting. You will see that none of the colors touch each other. Go to England, choose four colors to paint its regions called the counties, you will see it will be enough. You will be able to paint without any color touching each other. As a matter of fact, this idea was discovered while painting this exact map. Francis Guthrie, a botanist and mathematician, realized that 4 colors were enough while painting this map in the 1850s. He and his brother wrote a letter to De Morgan, the famous mathematician of the time. A student of mine asked me to day to give him a reason for a fact which I did not know was a fact-and do not yet. if a figure be any how divided and the compartments differently coloured, four colours may be wanted, but not more. the following is his case in which four are wanted
Query cannot a necessity for five or more be invented . . . it says any shape. So it doesn't even have to be a map. Even for completely made-up maps, we can say that 4 colors are sufficient. That's why today in the world of mathematics, this is called the "four-color map theorem" or simply the "four-color theorem". It is called so, but even big professors have difficulty in proving it. I just said that a mathematician discovered it. Then said that he send it to his brother first, and his brother to De Morgan. I’m saying “the De Morgan”. From De Morgan's laws and stuff. You may remember, you must have read it in high school. For example, they cannot prove it. However, they also realize such a reality, and for 125 years, many mathematicians and many professors have tried to prove it but fail. In this video we will not only understand this with you, but also learn how to solve it.
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Researched and Written by: Ögetay Kayalı
Organized and Presented by: Barış Özcan
Edited by: Alperen Çatak
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The full text of the video and the sources used:
barisozcan.com
3 окт 2024
