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How this simple theorem defeated 100 of mathematicians | 4 color map theorem
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Welcome to our channel! In this video, we dive deep into the fascinating world of the 4 Color Map Theorem, a mathematical puzzle that has intrigued mathematicians for over a century. Discover how this seemingly simple problem—proving that any map can be colored using just four colors without adjacent regions sharing the same color—stumped 1,000 mathematicians for 100 years!
What You’ll Learn:
The history and significance of the 4 Color Map Theorem.
Key mathematicians involved in solving this problem.
The groundbreaking proof that finally cracked the theorem in 1976.
Real-world applications of the theorem in various fields.
The Four-Color Theorem states that in any plane surface with regions in it (people think of them as maps), the regions can be colored with no more than four colors in such a way that two regions that have a common border do not get the same color. They are called adjacent (next to each other) if they share a segment of the border, not just a point.[1]
This was one of the first theorems to be proved by a computer, using a proof by exhaustion. In proof by exhaustion, the conclusion is established by dividing it into cases and proving each one separately. The number of cases sometimes may be very large. For example, the first proof of the Four-Color Theorem was a proof by exhaustion with 1,936 cases (in 1976). This proof was controversial because most of the cases were checked by a computer program, not by traditional mathematical arguments. The shortest known proof of the Four-Color Theorem today still has over 600 cases.
Even though the problem was first presented in 1852 as a problem to color political maps of countries, mapmakers are not particularly interested in it. According to an article by the math historian Kenneth May , “Maps utilizing only four colors are rare, and those that do usually require only three. Books on cartography and the history of map-making do not mention the four-color property.”
Many simpler maps can be colored using three colors. The fourth color is required for some maps, such as one in which one region is surrounded by an odd number of others, which touch each other in a cycle. One such example is given in the image. The Five-Color Theorem states that five colors are enough to color a map. It has a short, elementary proof and was proved in the late 19th century (Heawood 1890). Proving that four colors suffice turned out to be significantly more difficult. A number of false proofs and false counterexamples have appeared since the first statement of the Four-Color Theorem at University College London in England.
Now to know more watch out this full video till the end.
Thanks for watching.
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क्यों Graphs से डरते है Mathematicians | 4 color map theorem
FAIR-USE COPYRIGHT DISCLAIMER This video is meant for Educational/Inspirational purpose only. We do not own any copyrights, all the rights go to their respective owners. The sole purpose of this video is to inspire, empower and educate the viewers.
#4ColorMapTheorem #Mathematics
What You’ll Learn:
The history and significance of the 4 Color Map Theorem.
Key mathematicians involved in solving this problem.
The groundbreaking proof that finally cracked the theorem in 1976.
Real-world applications of the theorem in various fields.
The Four-Color Theorem states that in any plane surface with regions in it (people think of them as maps), the regions can be colored with no more than four colors in such a way that two regions that have a common border do not get the same color. They are called adjacent (next to each other) if they share a segment of the border, not just a point.[1]
This was one of the first theorems to be proved by a computer, using a proof by exhaustion. In proof by exhaustion, the conclusion is established by dividing it into cases and proving each one separately. The number of cases sometimes may be very large. For example, the first proof of the Four-Color Theorem was a proof by exhaustion with 1,936 cases (in 1976). This proof was controversial because most of the cases were checked by a computer program, not by traditional mathematical arguments. The shortest known proof of the Four-Color Theorem today still has over 600 cases.
Even though the problem was first presented in 1852 as a problem to color political maps of countries, mapmakers are not particularly interested in it. According to an article by the math historian Kenneth May , “Maps utilizing only four colors are rare, and those that do usually require only three. Books on cartography and the history of map-making do not mention the four-color property.”
Many simpler maps can be colored using three colors. The fourth color is required for some maps, such as one in which one region is surrounded by an odd number of others, which touch each other in a cycle. One such example is given in the image. The Five-Color Theorem states that five colors are enough to color a map. It has a short, elementary proof and was proved in the late 19th century (Heawood 1890). Proving that four colors suffice turned out to be significantly more difficult. A number of false proofs and false counterexamples have appeared since the first statement of the Four-Color Theorem at University College London in England.
Now to know more watch out this full video till the end.
Thanks for watching.
Social accounts link
क्यों Graphs से डरते है Mathematicians | 4 color map theorem
FAIR-USE COPYRIGHT DISCLAIMER This video is meant for Educational/Inspirational purpose only. We do not own any copyrights, all the rights go to their respective owners. The sole purpose of this video is to inspire, empower and educate the viewers.
#4ColorMapTheorem #Mathematics
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