Graph Theory: The Four Coloring Theorem "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
exploration, maps have helped people record the specifics of new and unexplored regions of the earth. The earliest maps were crudely drawn by hand and were rough estimates of geographic area based on interpretation of the land. Once people began coloring maps, to designate partitions within regions, the problem arose regarding the necessary number of colors it would take to color a map. II. History The theorem was first proposed by August Ferdinand Moebius in 1840. However, the problem was ignored
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
shop and restaurant thinks it can serve a latte. I've even seen coffee stands in drugstores. Unfortunately, these sources rarely have coffee worth drinking. A simple cup of drip coffee can be mastered by any novice. It's to coffee making what coloring in the lines is to art, a small challenge. It take a true coffee connoisseur to master the espresso or latte. I am proud to be such a connoisseur. Learning to make a proper cup of coffee is akin to an art apprentice learning under a great painter
dirt and grime of a hard days work, I caught myself staring into the mirror. I said to myself, "Gosh, I look horrible today." My hair seemed so dull, so bland. My face looked so pale, so white. My eyes were surrounded by a purplish blue coloring, the same coloring that I had attempted to hide that same morning with my makeup. My eye lids felt like they weighed a ton. "Damn! Mondays are really starting to wear me down. I got to start getting some rest." But that was not it, and I knew it. I lied to
me, however, since I didn't care much for them. I was in the store the other day, and ran into America's favorite snack again. The product hung in four-ounce bags near the bakery section of the supermarket. Bags of Cracker Jack? The package coloring was the same, the logo was still a boy in a sailor outfit accompanied by a dog: Sailor Jack and Bingo. It was 99 cents, and there was a surprise inside. Didn't it used to specify a "toy" surprise inside? I had known that for some time now,
zoo animals standing near by. The idea of this dish is to make the train look similar to the candy house in the story, "Hansel and Gretel". The first step was to add food coloring to the icing. She was excited. "Mommy, can I mix the colors?" Next, I decorated the cake board with grated coconut. I add green food coloring to the grated coconut. Jessica said, " Mommy, that looks like grass." Then, I decorated the carts of the train with different color icing. For example, I placed green, blue
The Visible Light Spectrum “Mr. Petersuh-uh-uhn…. I need a white crayon for the white parts of the map!”, my daughter’s classmate whines as she peers into her box of mismatched Crayons. “Don’t worry about coloring those parts of the map. White isn’t a color anyways…”, replies her sixth grade teacher. Uh-oh. Big mistake! The entire class is now in for an impromptu lesson in the properties of light and the visible spectrum, courtesy of the child of a laser student. Added bonus: elevated egg-headed
look like the ideal woman. We’re too misshaped, spotty, old, flabby, fat, skinny, or the wrong color. We go in for breast enhancement, liposuction, facelifts, nose jobs, skin color altering, we buy into certain fad diets, we purchase makeup and hair coloring and styling products, and the new exercise machine miracle worker. Beauty is a multi-million dollar operation that can’t afford for any women to love themselves as they are. The current beauty ideal for women, tall, very thin,... ... middle
Teachers. The first known bubble gum appeared in 1906, and was a dud. Known as Blibber Blubber, it was sticky, brittle, and insufficiently cohesive. In 1928, an accountant, Walter Diemer, invented an improved version of bubble gum. The only food coloring he had on hand was pink, so for many years, pink was the common color of bubble gums. Diemer arranged to market the bubble gum in Philadelphia candy stores and the product became wildly popular with children. Fleer Company purchased the recipe, and
upon by agents other than sexual recombination. For example, take a population of mice that consists of 1,000 members. A specific allele, albino allele, is recessive within this species. 80% of the population expresses the normal phenotype- brown coloring, while the remaining 20% are albino. 640 members of the population have the genotype AA, 320 have Aa, and 40 have aa. If completely random mating were to occur, there would be an 80% chance that a gamete would bear the normal allele, A, and a 20%
any television would ever be. The ad itself is fairly large, taking up four full pages, which feel a little bit thicker than the pages in the rest of the magazine. Many people will notice the ad not only because of its size but also because of its coloring. All four pages of the ad are filled with eye-catching green grass and a bright blue sky. On the first page, lying on top of the grass are various models of the High Definition Televisions from Samsung and a playful looking girl with her back turned
Cosmetology Cosmetology is working with skin, hair and nails. Which includes things like hair styling, cutting, coloring, shampooing, manicures, waxing, facials, etc. "More than a half a million people work as cosmetologists." (Careers For Woman Without College Degrees 254) It is a great profession for people who would like to have a career in the beauty industry. It's a great career for a mother in a two income family or if you're just living on your own. This career is not only for woman, it
changing again. I gasp, intrigued. “That’s the beautiful part,” my grandfather observes. “It’s beautiful when it’s turning.” The challenge of cleaning out my desk drawers in preparation for the move to New York results in my stumbling across an old coloring book. I leaf through the pages, startled by the number of pictures I’d left only partially colored. With quick, shaky movements, it seems as if I had simply jumped from shading one image to the next, as if there were something complete about leaving
The Ghost’s Appeal: Man’s Interest in the Superficial in Toulouse-Lautrec’s At the Moulin-Rouge Henri de Toulouse-Lautrec’s famous painting, At the Moulin-Rouge, combines striking coloring with abnormal lighting to create a work that addresses men’s superficial interest in women. The dark scene depicted in the painting includes ten people scattered about a restaurant. In the center, two women and three men sit casually around a table while the background portrays two men and a woman peering into
wavelengths, often in the visible region. In fireworks, the energy to excite the electrons comes from the reaction between the oxidizer and fuel. Fireworks are usually made out of the following items; an oxidizing agent, a fuel (reducing agent), a coloring agent, binders and regulators. These mixed together are what make up the basic fireworks: Oxidizers The first thing in a firework is the oxidizing agent. These produce the Oxygen to burn the mixture. Oxidizers are usually nitrates, chlorates
on a firm foundation of symbolism. Nature, color and light are used as symbols throughout the novel to illustrate several areas of the story (Waggoner 154). The prison door, for example, was described as being composed of “oak and iron” and its coloring “sad” and “gray”, symbolizing the rigidity of the Puritan society against sinners (Waggoner 154). The rosebush situated outside of the prison door is like a “moral blossom” growing amongst the bitter weeds of society, in the “most unlikely of places”
with more than 560,000 visits per month. (Doubleclick.) This section really takes advantage of what multimedia has to offer. When you enter the site music begins to play, and animated graphics begin to move. The site contains games, an interactive coloring book, and ideas for arts and crafts projects. It also has links to all the children's shows that are on PBS including, Sesame Street, Barney, and Thomas the Tank. Its design is extremely colorful, playful, and intriguing. Another main section in
with solid black blotches. Coat color and patterning are associated with it’s habitat. 1. Savannah Leopards – Reddish to orange color 2. Desert Leopards – Pale cream to a yellow-brown coloring, The ones from cooler regions a more grayish color. 3. Rainforest Leopards – dark, deep golden coloring 4. High mountain Leopards – even darker than 3 Black Leopards/Black Panthers are found most frequently in humid forests but are just a color variation and not a subspecies. Variations in
relationship of one-ness Miss Brill has with her own fur. Through Miss Brill's description of the woman in the ermine toque, it is clear that Miss Brill perceives the woman in connection with the fur she wears (441-442). Miss Brill compares the woman's coloring to the color of her fur by pointing out that everything, her hair, her face, even her eyes, [is] the same colour as the shabby ermine"(441). Miss Brill goes on to describe the woman's hand as being "a tiny yellowish paw" (441). And when the woman