The Golden Ratio Essay Example for Free

The Golden Ratio Essay The Golden Ratio is a fascinating number which can be found almost everywhere –from nature to architecture to art. To 18 decimal places, it has a value of 1. 618033988749894848 but is usually shortened to 1. 618 much like ? is usually rounded off to 3. 1416 (Powis, n. d. ). Signified by the letter Phi (? ), the Golden Ratio can be simply defined as â€Å"to square it, you just add 1† (Knott, 2007). Written in mathematical equation, this definition becomes ? 2 = ? + 1. When the resulting quadratic equation ? 2- ? 1=0 is solved, there are two solutions: 1. 6180339887†¦ and -0. 6180339887†¦. Notice that the two solutions have identical decimal parts. The positive number is the one considered to be the Golden Ratio. Another definition for ? is â€Å"the number which when you take away one becomes the value of its reciprocal† (Powis, n. d. ). Notice that the value of the reciprocal of 1. 618 (1/1. 618) is 0. 618 which is just one less than the Golden Ratio. The Origins of the Golden Ratio Euclid of Alexandria (ca. 300 BC) in the Elements, defines a proportion derived from the division of a line into segments (Livio, 2002). His definition is as follows: A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser. In order to be more understandable, let’s take Figure 1 as an example. In the diagram, point C divides the line in such a way that the ratio of AC to CB is equal to the ratio of AB to AC (Livio, 2002). When this happens, the ratio can be calculated as 1. 618. This is the one of the first ever documented definitions of the Golden Ratio although Euclid did not call it such at that time. A C B Figure 1. Point C divides line segment AB according to the Golden Ratio The Golden Ratio 3 The Golden Ratio in Art and Architecture Throughout history, the Golden Ratio, when used in architecture, has been found to be the most pleasing to the eye (Blacker, Polanski Schwach, n. d. ). Rectangles whose ratio of its length and width equal the Golden Ratio are called golden rectangles. The exterior dimensions of the Parthenon in Athens, sculpted by Phidias, form a perfect golden rectangle. Phidias also used the Golden Ratio extensively in his other works of sculpture. The Egyptians, who lived before Phidias, were believed to have used the ? in the design and construction of the Pyramids (Blacker, Polanski Schwach, n. d. ). This belief however has both supporters and critics. Theories that support or reject the idea of the Golden Ratio being used in the construction of the Pyramids do exist it is up to the reader to decide which ones are more reasonable (Knott, 2007). Many books also claim that the famous painter Leonardo da Vinci used the Golden Ratio in painting the Mona Lisa (Livio, 2002). These books state that if you draw a rectangle around the face of Mona Lisa, the ratio of the height to the width of the rectangle is equal to the Golden Ratio. There has been no documented evidence that points to da Vinci’s conscious use of the Golden Ratio but what cannot be denied is that Leonardo is a close personal friend of Luca Paciolo, who wrote extensively about the Golden Ratio. Unlike da Vinci, the surrealist painter Salvador Dali deliberately used the Golden Ratio in his painting Sacrament of the Last Supper. The ratio of the dimensions of his painting is equal to ? (Livio, 2002). The Golden Ratio in Nature The Golden Ratio can also be found in nature. One of the most common examples is snail shells. If you draw a rectangle with proportions according to the Golden Ratio then consequently draw smaller golden rectangles within it, and then join the diagonal corners The Golden Ratio 4 with an arc, the result is a perfect snail shell (Singh, 2002). There have also been ongoing debates and conflicting research results regarding the relationship of beauty and  in humans. Some argue that human faces whose dimensions follow the Golden Ratio are more physically attractive than those who don’t (Livio, 2002). With conflicting results aside, the existence of the Golden Ratio just shows that beauty (whether in art, architecture or in nature) can be linked to mathematics. The Golden Ratio 5 References Blacker, S. , Polanski, J. and Schwach, M. (n. d. ). The golden ratio. Retrieved October 8, 2007 from http://www. geom. uiuc. edu/~demo5337/s97b/. Knott, R. (2007). The golden section ratio: Phi. Retrieved October 8, 2007 from http://www. mcs. surrey. ac. uk/Personal/R. Knott/Fibonacci/phi. html. Livio, M. (2002). The golden ratio and aesthetics. Plus Magazine. Retrieved October 8, 2007 from http://plus. maths. org/issue22/features/golden/index. html. Powis, A. (n. d). The golden ratio. Retrieved October 8, 2007 from http://people. bath. ac. uk/ajp24/goldenratio. html. Singh, S. (2002 March). The golden ratio. BBC Radio. Retrieved October 8, 2007 from http://www. bbc. co. uk/radio4/science/5numbers3. shtml.

My Life Essay -- Personal narrative, descriptive Essays

Road trips make for great writing, especially if you are driving alone. All you have is the road and your thoughts. Even the radio is turned off eventually, as silence takes precedent. This was my experience a few weeks ago, driving home from a pseudo-family reunion. My first thoughts were basic; what I had to do the following week, how great it had been to see all my friends, and how good Jordan had looked that weekend. Yet, as my drive progressed, my thoughts began to wander. I began thinking about my life; what I had already accomplished and what was still waiting for me. I realized that there are so many things that I want to do before I die. I quickly sorted through them in my mind and this is what I discovered. I want to visit the 7 Wonders of the World; walking along the banks of Victoria Falls and standing beneath the shadow of the Sphinx. These are some of the most amazing structures in the world, and I need to experience them for myself, instead of through books and photographs. I want to use my time to help others. There is an amazing organization called Sa...

Alice Walker: The Welcome Table Essay

Through literature we are able to learn about different meanings and other human experiences. â€Å"Literature influences each individual differently† (Clugston, 2010). In Alice Walker’s short story The Welcome Table, it allowed the readers to read and learn about how, and what life was like for an elderly black lady during the 1960s. During these times blacks were discriminated against and the cruel treatment that they endured as human beings was unnatural and unheard of to us in this day and time. In this short story by Ms. Walker, it portrays to the readers how during this time period the African Americans were treated. The reason that this story caught my attention was due to the fact that the elderly lady that is portrayed in the story was so cruelly discriminated against for entering a white church. As you read this story, one cannot help but be intrigued by how the story speaks about the elderly lady and how she has lived her life and had been treated her whole life. Alice Walker starts the story off with the woman getting ready to attend church and the clothes that she is dressed in, you knew she had no money. â€Å"The old woman stood with eyes uplifted in her Sunday~GO~TO~ meeting clothes: high shoes polished about the tops and toes, a long rusty dress adorned with an old corsage, long corsage, long withered, and the remnants of an elegant silk scarf as headrag stained with grease from the any oily ponytails underneath.† (Walker,1967) This poor lady had lived a hard life and it showed on her face and body, so you could tell she knew suffering. The story tells us that this old lady stumbles into an all white church from the freezing cold. The poor white people just stared at her in pure disbelief as though she had committed a crime for entering their church. In the reading it stated â€Å"And so they gazed nakedly upon their own fear transferred; a fear of the black and the old, a terror of the unknown as well as of the deeply known.† (Clugston, 2010) This shows from the sentence, the way the congregation looked at the elderly lady, they were afraid of African-Americans at this time period for no reason that they could even fully understand. They meaning the white community did not like blacks and they were treated unjustly at all times and any cost. The way that the black people were treated back in the 1960s and even before the 1960s, the African-American people were not treated or respected like the white people. To read a story like this, helps me to understand the struggle and pain that the woman endured, as it was told by the narrator or persona of the reading. Some of the people felt as if the beginning of the end of worshipping of the Holy Church and as an invasion of their privacy. Many felt also as if they had lost their privacy now that she had entered their place of Holy Worship. As, I bring this to a close we have to remember that no matter whom or where we are in the world today, we should not pass judgment on another person just because of how they dress, their ethnic background, or where they may live. The story portrayed an elderly black lady who was forgetful and showed her struggle through her eyes and body still walked down the road about a half mile to this church to worship the lord. Even though she was thrown from the church, she did not stop singing and talking to her God. To me, this shows us that no matter our struggle we should never stop believing in what we believe just because someone else does not want us to. Reference Clugston, R.W. (2010). Journey in literature. Retrieved from https://content.ashford.edu Walker, Alice, (1967). The Welcome Table. Retrieved from http://web.ebscohost.com.proxy-library.ashford.edu/ehost/delivery?isd=72e76da8-5292-49 Retrieved 1/16/2013 Walker, Alice, (1967). The Welcome Table. Literary Cavalcade; Feb 2003;55-5; Proquest Central, Retrieved 1/16/2013

Chapter Analysis Harry Potter - 985 Words

Audrey Loeffler Fields English period 1 March 9, 2014 Forget Harry Potter, This is the Boy Who Lived Pi is an incredible individual. He went on an inconceivable journey that changed him mentally. There was no way he would come back the as the same person. After going through a shipwreck, he refuses to believe that he might really be stranded. When he acknowledges that he really is lost, Pi kills for the first time for the sake of survival. His physical and religious limits are tested immensely and it transforms him forever. Pi has a definite reason to go on this journey. He explains his shock upon discovering the sinking ship, â€Å"I couldn’t believe my eyes. What was this water doing here?†¦ Down there was where my family was† (Martel 129). It was that he had no choice. Pi’s life was thrown head first into a shipwreck, his happiness ground to a halt. He lost his family in his call to adventure. He has nothing to lose, until his shock drives him to near insanity, â€Å"Ravi was right. Truly I was to be the next goat. I had a wet, trembling, half-drowned, heaving and coughing three-year-old adult Bengal tiger in my lifeboat† (Martel 124). Shock is a powerful thing. Pi was so stunned he did not realize that he was helping a tiger into his lifeboat until it was too late. There is now absolutely no way Pi will not have an adventure. Staying alive is adventure enough. That is not to say Pi wants an adventure. Pi’s wants, his desires for a normal life with his family has clashed with theShow MoreRelatedThe Way Of The World Essay1580 Words   |  7 Pagesbecomes more fragmented in novels. The Following four works; â€Å"Harry Potter and the prisoner of Azkaban†(1999), â€Å"The David Copperfield†(1850), â€Å"The Prime of Miss Jean Brodie†(1961) and â€Å"Dead Poets society†(1989) are defined as the literary genre ‘Bildungsroman’ in different Medias. Each of the works has different analysis of Bildungsroman as the methods of maturity. 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