Name: Marina Thomas Date: 10/17/14 Research Paper Draft

Topic:The Golden Ratio

So why is it that Angelina Jolie is so gorgeous or why is the Mona Lisa a perfect work of art? Art and beauty is just one of the many pleasures of life. However, it is unlikely for someone to ponder on the detail of this beauty which in fact relates to mathematics. The Golden Ratio or Rectangle is believed to make the most pleasing shape. The golden ratio is approximately equal to 1.618. It is actually an irrational number that continues on called phi. Phi can be shown as ? or ?. The golden ratio is expressed as a rectangle that can be applied in many areas of life today. This includes architecture, art, and geometry. The golden ratio can be applied…

This is known as the Golden Spiral. This spiral is supposedly pleasing to the eye and is actually applied in many forms of nature. Some examples include pinecones, seashells, flowers and even the human face. A major example is the sunflower. A spiral is formed in the center where seeds are formed or are growing. Once a new cell has formed, the spiral turns. As many seeds possible is squeezed with the absence of any possible gaps. “In order to optimize the filling, it’s necessary to choose the most irrational number there is, that is to say, the one the least well approximated by a fraction. This number is exactly the golden mean.” (http://www.popmath.org.uk/rpamaths/rpampages/sunflower.html) The Golden Ratio also in fact, has a connection with proportion, presumably the human body. Leonardo Da Vinci referred to it as the Divine Proportion. He had used this mathematical form in his art, for example, the Vitruvian man. Three Golden Rectangles are found upon the head, torso and legs. A person’s eyes are Phi of a distance apart from the human’s chin. You can even find the Golden spiral upon the ears of a person, furthermore, making our ears proportional. Based on the original idea of the golden ratio a comparison of any two two aspects will be led to proportion in an ideal way. Examining A and B algebraically,it has to be such that A + B divided by A=A divided by B. It is then identifiable that a comparison will result in the ratio 1:1.618. It is able to be found all over the human body. For example, if the hand has the value of 1, then naturally, 1.618 will become the result for the combination of both the forearm and the hand. Going down to the lower body, the same situation is found. If the foot is found with the value 1 then the combination of both the foot and the shin will be found to equal 1.618. The face is probably the strongest point of…