This work is based on one of the most famous problem in mathematics: four color theorem. In the introduction, history and examples of the applications of the four color theorem have been examined. Beside the big history of it, four color theorem has a huge application area e.g. in coloring questions, mobile phones, computer science, scheduling activities, security camera placement, wireless communication networks etc. In this work, an application of four color theorem in a specific area has been examined: location area planning. Therefore this essay tries to answer this following question: ‘What are the applications of four color theorem in location area planning?’
Four color theorem is first proposed on October 23, 1852 by Francis Guthrie.
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Another name of the problem is Guthrie’s problem after Francis Guthrie, who first realized the theorem in 1852. Francis Guthrie was trying to color the map of countries of England and then he noticed that four colors sufficed. He asked his brother Frederick whether it was true that needed at least four colors to color a map of the counties of England. All of these methods was used by other mathematicians to make progress on the four-color problem. There are six and five color theorems in mathematics and they have official proves. But to reduce the number of colors from five to four is very difficult. This problem was finally proved by Appel and Haken (1977), they constructed a computer-assisted proof that four colors were sufficient. However some mathematicians do not accept it because it includes comprehensive analysis by computer that cannot done by hand. But the proof is still valid because no errors found yet.
Today, mathematicians are still looking for a new, computer-free solution for four color theorem, and graph theory is one of the main methods used in these studies. I prepared for Math Olympiads in last 5 years, and one of the topics I exposed while studying was graph theory. I have an interest to this problem therefore I decided to write my extended essay about four color theorem. There is an approach to the solution of the four color theorem with graph theory in this
Two human receptor-making genes are similar to those in other mammals. This implies that human color vision began when one of the genes in other mammals duplicated and copies specialized over time for different light sources. The switch to color vision correlates to a switch from a monochromatic forest to one with a multitude of colors in
In the beginning, the book opened with the social, economic, and political struggle of African Americans. The experience was extremely gruesome for both the enslaved and new generation of freed slaves. As the years passed, the oppression became worse for people of color even though they were free there were several stipulations put in place to hold them back from succeeding. The University of Chicago immediately recognized the major hitches with discrimination and decided to move forward with implementing studies for social research better known as the “Chicago School”. These studies showed that although African-Americans were going through a social disadvantage.
In the novel, Death By Black Hole, Neil DeGrasse Tyson proves that the common assumption that the color of our solar system’s sun is yellow, is, in fact, an incorrect belief. Many people think that the sun is yellow because, “Near sunset … the blue light from the sun’s spectrum, lost to the twilight sky, leaves behind a yellow-orange-red hue…”(Tyson 293).This shows why this common misconception is not an easy thing to spot and is understandable why most people incorrectly assume the color of the sun. The actual color of the sun is proven by the fact that, “ if the sun were yellow… then white stuff would reflect this light and appear yellow…”(Tyson 293). If the sun was actually yellow then the colors we see around us would have been changed
Kevin Jimenez Ms.Marder English 3cp 8 April 2016 The Great Gatsby:True Colors Life is all about feelings and emotions and what better way to describe them using colors. Colors are often used to describe symbolism they describe the mood of the setting and they can also differentiate the rich from the poor,colors are used in different aspects to describe someone or something. In F.Scott Fitzgerald’s The Great Gatsby, characters such as Gatsby Nick and Daisy use colors to describe their emotion of the setting, and feelings towards each other. Colors portray each character 's emotions, setting changes, and foreshadowing future events.
Seeing Maycomb in Color In the film adaptation of the book To Kill a Mockingbird by Harper Lee, the scene where Scout and Dill have a talk with Dolphus Raymond is not shown. The scene takes place at Tom Robinson’s trial, when Dill and Scout go outside after Dill becomes upset with how Tom Robinson was being treated. Scout has a hard time understanding why Dill is so upset, but an infamous man from town, Dolphus Raymond, comes to console Dill and says he agrees. Him and Scout proceed to have a very eye opening conversation, where Scout discovers Dolphus Raymond is not a drunk like everyone thought, but is just pretending to be one to put others at ease.
Gold and money, a light in the dark, or a warning on the road; the color yellow has many diverse meanings in society and these are just a few. In The Great Gatsby by F. Scott Fitzgerald colors represent several aspects of the characters as they are swept through rollicking emotions powered by the mystery shrouding the enigmatic Jay Gatsby in the height of the Roaring Twenties. Yellow gives insight into Gatsby’s character, who he wants to be, who he is in truth, and who others think he is. The color yellow is often associated with money because it reminds people of gold. In Fitzgerald’s book, the colors gold and yellow are used interchangeably and often to connotate class or wealth.
Color Guards’ Amazing History! People know that during half time at football games two bands play and in the band there are the color guard. No one ever stops to think about them and how they came to be. The fans just know that they are there most likely to just entertain them. They never stop to think twice as to how color guard was made and the big meaning behind it all.
Imagine helping a deaf person hear music and helping them feel the emotion just by watching the color guard perform from the stands. That is what color guard is. Every year I join color guard not knowing what I am getting myself into. Although I am in color guard and I know things about it, there is a lot that I am missing. I know it consists of dance, flag, rifle, and sometimes saber.
Even then, Kempe's paper helped other mathematicians to attack this problem using various approaches. Finally, after more than a century passed since the problem came into existence, in the year 1976, two mathematicians Wolfgang Haken and Kenneth Appel~\cite{kapp76}, taking the help of a computer, proved that the conjecture was indeed true. The proof consisted of a rather short theoretical section, four hundred pages of detailed checklists showing that all relevant cases had been covered, and about 1800 computer runs totaling over a thousand hours of computer time. However, not many accepted this proof partly because of the extensive use of computers in it and partly because of its extraordinary length. After this, several versions of the proof of the Four Color Theorem came into existence out of which the most acceptable and well-structured was given by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas~\cite{nrob96} in the year
At the heart of whiteness studies is the invisibility of whiteness and white privilege (Ahmed, 2004). Whiteness is thought of as the hidden criterion to which every other race is measured against. Through the lens of whiteness, the “other” is seen as deviant (Ahmed, 2004). The invisibility of whiteness, however, is only from the perspective of those who are white (Matthews, 2012). To people who are not white, it is pervasive and blatant.
Item 2: Color Chart: In the book “The Great Gatsby,” by F. Scott Fitzgerald, colors have been used to represent the character’s unapparent and underlying thoughts, feelings, status and class. Through the motif of colors, Fitzgerald depicts the feelings of the character as he refers to a specific color while describing each one of them. The colors make a deep impact on the readers as they contain a profound meaning throughout the novel. There are around five main colors in the novel appearing frequently: white, yellow, green, blue and grey, which help the novel look more gaudy and idealistic.
" This overall shows the different colors based on the different systems and classes of the society. Huxley add in colors to separate others and to distribute across the civilized new world. From this, they are each labeled to a different
Also, different colours have been used to make other objects stand out. An example of this is that the children in the background stand out because the author has used a darker colour than the surrounding earth and the sun stands out because it is a brighter colour than the surrounding blue for the
The origins of human skin colour: The origins of human skin colour remained an enigma that was to generate a multitude of misconceptions. The true source of human pigmentation was finally revealed with the discovery of the melanocyte in the 19th century. Once the amino acid tyrosine was identified to be the key enzyme in pigment formation, attention focused on elucidating the chemical structure of melanin, an enterprise that remains incomplete.
Hair coloring is the practice of changing of hair color. People color hair for cosmetic reasons to cover up gray or white hair, to change their appearance, to be more fashionable, or to restore the hair to its original natural color after it has been bleached by the sun or previous coloring. There are many different types of hair color. Semi permanent, Demi permanent, and Temporary. You can buy chalk that will color your hair, some even be done professional or at home.