1. NAME: MUQSIT HAIDER 7T GOLDEN RATIO MIRACLE OF KAABA

2. WHAT IS GOLDEN RATIO? two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0,

3. GOLDEN RATIO IN NATURE? The famous Fibonacci sequence has captivated mathematicians, artists, designers, and scientists for centuries. Also known as the Golden Ratio, its ubiquity and astounding functionality in nature suggests its importance as a fundamental characteristic of the Universe in nature.

4. GOLDEN RATIO IN IN ANCIENT ARCHITECTURE? Le Corbusier explicitly used the golden ratio in his Modular system for the scale of arcitectural proporation. He saw this system as a continuation of the long tradition of Vitruvius Leonardo da Vinci's “Vitrvian Man”, the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of arcitcture.

5. KAABA IS GOLDEN MEAN OF EARTH? It is a miracle that Mecca’s / Kaaba’s place on earth is designed by the verse in the Holy Quran, Muslim’s holy book for over 14 centuries and it states that in this holy area the evidences are lurked in that will cause communities’ searching for the right way. It proves that it is written by a force that knows the golden ratio, can see the earth from the space and knows the measurements that are accepted in the future, knows math very well, God. It is the mean point of earth.

6. METHAMETICAL PROOF? Therefore, if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates φ ; e.g., 987/610 ≈ 1.6180327868852. These approximations are alternately lower and higher than φ, and converge on φ as the Fibonacci numbers increase, and: More generally: where above, the ratios of consecutive terms of the Fibonacci sequence, is a case when. Furthermore, the successive powers of φ obey the Fibonacci recurrence:recurrence This identity allows any polynomial in φ to be reduced to a linear expression. For example: The reduction to a linear expression can be accomplished in one step by using the relationship

7. CONCLUSION After conducting my experiment, I discovered the hypothesis that "I believe that the closer an object or face approximates phi, the more aesthetically pleasing it will be because of the presence of phi in human proportions, the natural world, and art" was correct. I surveyed 60 students, over 25% of the population at City School. This is a large enough portion of students to reflect the whole population. More students preferred the painting, rectangle, and set of flowers that approximated the Golden Ratio than otherwise. The majority of students, 41.7% preferred the Golden Rectangle over the square and elongated rectangle. 61.7% of students preferred flowers with Fibonacci numbers of petals to flowers whose petals don't show Fibonacci. 53.4% preferred The Last Supper, painted with the Divine Proportion in mind, to the painting Nighthawks. This evidence shows that, whether consciously or unconsciously, the Golden Ratio affects our perception of aesthetics. Other data regarding facial beauty showed lopsided results. 70% of people preferred the male face that approximated phi, while 66.7% of people preferred the female face that didn't approximate phi. These results I have chosen to exclude from my analysis, because of personal preferences, including hair, eye color, eye shape, facial hair, and facial recognition, that could have effected the results. Also, many people were uncomfortable choosing which face was more attractive in front of others. If I were to perform a second trial, I would have answers be anonymous, and test equal numbers of each grade and gender. This study has also made me interested in what other factors effect affect attraction, and what causes people to be attracted to one another. I am also interested in why the Golden Ratio is so abundant in different elements of life.