The Mathematics of Map Coloring
The four-color conjecture has been one of several unsolved mathematical problems. From 1852 to this day, practically every mathematician has studied the problem long and hard, but to no avail. The conjecture looks as though it has been solved by Wolfgang Haken and Kenneth Appel, both of the University of Illinois. They have used computer technology to prove the conjecture. The calculation itself goes on for about 1200 hours. The staggering length of the computation of the proof is what creates some controversy in the mathematical world. The Appel-Haken Theorem is based on numerous assumptions, “that there is an overwhelmingly great probability that their method of proof must succeed.” [3] It assumes that the theory itself is correct, but the theory itself is also an assumption. You can see why this issue has been wreaking havoc for many years.
It all started back in 1852 when Francis Guthrie was coloring a map of England. He wanted to know the least amount of colors, or chromatic number, it would take to color the map so no two adjacent regions are of the same color. He found the chromatic number to be four. He then studied arbitrary maps and wondered if all maps could be colored with four colors. Francis’ curiosity would be in the minds of all mathematicians to come. He then passed this question on to his brother, Frederick. He then submitted this to his professor Augustus deMorgan as a mathematical conjecture.
deMorgan was fascinated by the Four-Color problem and wrote in a letter to his colleague Sir William Rowan Hamilton the next day after seeing the conjecture. Hamilton was less enlightened by it, and never worked on it. It was through deMorgan that the Four-Color problem was made known, thus deMorgan has incorrectly been dubbed the originator of the problem.
Eventually the hype surrounding the conjecture died down in the early 1860’s. This down time, during which interest in the problem was minimal, only lasted about twenty years. A lawyer by the name of Alfred Bray Kempe proposed a solution in The American Journal of
E. D. Hirsch and Lisa Delpit are both theorist on teaching diverse students. Both of these theorist believe that when teaching diverse students, teachers need to see their students for who they are. Seeing your students for who they are, means you look past the color of your students’ skin and recognize their culture. According to Stubbs, when teachers look at their students equally, no matter the color of their skin, then the teacher is considered colorblind (2002). Being colorblind is not a great thing because we should not treat all of our students the same, since each student is different. It is important to see our students for who they are because our classes are unique. Instead, our classes represent a rainbow underclass. According to Li, the rainbow underclass is the representation of families who are culturally diverse and economically disadvantaged (2008). In order to meet these student’s needs, teachers need to think about the struggles that each student face.
One atom may not have color but once many atoms come together and are stacked and ordered in the correct way they can start to show color. Color, therefore, is a property of relatively complex objects. Emergent colors do not play a role in color science especially if an individual atom does not have color. They satisfy the prejudice in favor of color realism. The biggest critics of color skepticism are the common people. They are a bit outraged to see some denying something that seems so basic. They figure if they see colors they must be there. Therefore, to most defending color skepticism is impossible because people are so convinced that color exists even before the color skeptic’s argument is presented. The spotty world argument helps to defend color skepticism. If one went through life seeing spots everywhere they would think that spots truly did exist in the universe. However, if this person went to an eye doctor and found that impurities existed in their eyes that make the world look spotty, this person would agree that their eyes deceived
was first conceived by Michael Faraday in the year 1832 in his Backerian Lecture to
He began writing about his hypothesis/ idea in 1864-65, and published the results in 1866. It was not until 1900 that his published findings were
Procrastination has become such a bad habit for me. It is very hard to stop procrastinating everything once you have gotten into the habit of doing it. Once I had a term paper due for my religion class. It was to be ten pages long and we were told to spend a lot of time doing it. Being the procrastinator that I am, I waited to the very last minute to do it. I waited until the night before to do most of it. Needless to say, I was up very late that night. In this class there was always a part of the paper due on a certain date before the final paper was due. Having things due before the final paper is due keeps me on task and keeps me from procrastinating until the day before the paper is due. There was one paper which we had to get sources for a while before the paper was due and it forced me to keep up with the paper, rather than let it go to the last minute. This class has taught me that the earlier you start the more positive your final result will be.
My thoughts were that because of this discovery psychologist after him were able to expand on his research and make today what it is. Other people might say that it isn’t possible to know how intelligent a brain is from just one test but really the test is just estimation and shouldn’t be taken literally. Currently Alfred Binet works it still being used to base current intelligence tests of off. Alfred Binets' work has been used my many other psychologists to make other intelligence tests.
Losing weight isn’t always easy and people often find it hard to stay with a diet that they choose because of the time consuming process of actually shedding pounds. Many fad diets, diets which raise and decrease in popularity, promise quick weight loss and so does The Cabbage Soup Diet. Being able to lose up to ten pounds in one week is a great accomplishment, and with The Cabbage Soup Diet, you can do just that.
John Forbes Nash Jr. is recognized as one of the most intelligent men in history. He is a Nobel Laureate (Charles 21). He is a holder of an honorary appointment in mathematics at Princeton University (Nasar 310). He is the man character of a film that ended up winning the Academy Award for Best Picture in 2000 (Oscar Legacy: Past Winners). By the way, he has also been diagnosed with schizophrenia (Nasar 16). It is a shame that such a brilliant man could acquire an illness that only one percent of the global population carries (Begley 44). However, his ability to see things that others couldn't was part of his gift as well. That's why he was able to make so many important contributions to society. His work with game theory was revolutionary and his invention of the game Hex was pretty cool as well (Nasar 76). His life was filled with drama and he still ended up successful in the end. His story is one that truly deserves to be immortalized on film. However, films are hardly ever completely accurate. Blockbuster films such as A Beautiful M...
The Greek poet, Hesiod, once said not to “put your work off till tomorrow and the day after (Jaffe, 2013).” According to the Cambridge dictionary, procrastination is the putting off of something important. When one first sees Hesiod’s quote, it sounds as if it is just one of those phrases that have been repeated so much that it has lost virtually all meaning. Hesiod’s quote reveals that procrastination has been around for a really long time, and since early times, people have tried to warn against it. De Paul professor, Joseph Ferrari discovered that up to 20% of people are chronic procrastinators(Jaffe,2013). That is not including the rest of the population that fall between occasional procrastinator and the procrastinator that does it just to see what they can get away with. There are many causes that can lead to procrastination, which is a hint as to why it is such a big issue. The result of those causes is procrastination, which is not without consequence. Procrastination can lead to a decline in one’s mental and physical health, mental stability, and emotional well-being. However, along with those negative effects, there are ways to combat procrastination.
"Every planar map is four colorable," seems like a pretty basic and easily provable statement. However, this simple concept took over one hundred years and involved more than a dozen mathematicians to finally prove it. Throughout the century that many men pondered this idea, many other problems, solutions, and mathematical concepts were created. I find the Four Coloring Theorem to be very interesting because of it's apparent simplicity paired with it's long, laborious struggle to be proved. There is a very long and eventful history that accompanies this theorem.
My past experience of procrastinating caused me to nearly fail a class, due to letting the gratification monkey get a hold of me. Even though, Tim Urban in his article, “Inside The Mind Of A Master Procrastinator,” discusses the entities of procrastination. Unfortunately, procrastination can cause many health problems, physical and emotional. Procrastination can make a person feel a sense of self-reliance. Finally, managing tasks in order of importance allows a person to gain more control over their sleep, health, as well as their outcome of tasks. At the end of the day it is about getting it
People who procrastinate overtime have it as a deeply ingrained habit. Are there ways to put off and avoid procrastinating? Off course there are. Knowing that you are procrastinating is the first step. Making efforts to stop is the greatest thing you can do for yourself.
Carl Friedrich Gauss was born April 30, 1777 in Brunswick, Germany to a stern father and a loving mother. At a young age, his mother sensed how intelligent her son was and insisted on sending him to school to develop even though his dad displayed much resistance to the idea. The first test of Gauss’ brilliance was at age ten in his arithmetic class when the teacher asked the students to find the sum of all whole numbers 1 to 100. In his mind, Gauss was able to connect that 1+100=101, 2+99=101, and so on, deducing that all 50 pairs of numbers would equal 101. By this logic all Gauss had to do was multiply 50 by 101 and get his answer of 5,050. Gauss was bound to the mathematics field when at the age of 14, Gauss met the Duke of Brunswick. The duke was so astounded by Gauss’ photographic memory that he financially supported him through his studies at Caroline College and other universities afterwards. A major feat that Gauss had while he was enrolled college helped him decide that he wanted to focus on studying mathematics as opposed to languages. Besides his life of math, Gauss also had six children, three with Johanna Osthoff and three with his first deceased wife’s best fri...
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
The Fibonacci Series was discovered around 1200 A.D. Leonardo Fibonacci discovered the unusual properties of the numeric series, that’s how it was named. It is not proven that Fibonacci even noticed the connection between the Golden Ratio meaning and Phi.