Lesson 16 Golden Section - The Golden Section ILLL Dr Shobha Bagai University of Delhi THE GOLDEN SECTION He felt himself suddenly reeling back to

Lesson 16 Golden Section - The Golden Section ILLL Dr...

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The Golden Section ILLL Dr Shobha Bagai University of Delhi
THE GOLDEN SECTION He felt himself suddenly reeling back to Harvard, standing in front of his “Symbolism in Art” class, writing his favorite number on the chalkboard . 1.618 …………………….. “This number PHI,” Langdon continued, “one-point-six-one- eight, is a very important number in art. Who can tell me why?” …………………….. “Actually,” Langdon said, “Stettner ʼ s right again. PHI is generally considered the most beautiful number in the universe”. …………………….. “Yes PHI,” Langdon replied. “One-point-six-one-eight. Want another example? Measure the distance from your shoulder to your fingertips, and then divide it by the distance from your elbow to the fingertips. PHI again. Another? Hip to floor divided by knee to floor. PHI again. Finger joints. Toes. Spinal divisions. PHI. PHI. PHI. My friends, each of you is a walking tribute to the Divine Proportion.” The Da Vinci Code by Dan Brown Geometry has two great treasures: one the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold, the second we may name a precious jewel. – Johann Kepler DISCOVERY OF THE GOLDEN SECTION There are many different names for the golden section; The Golden Mean, Phi, The Divine Section, The Golden Cut, The Golden Proportion, The Divine Proportion, and The Golden Ratio. The Great Pyramid of Giza built around 2560 BC is one of the earliest examples of the use of the golden ratio. The length of each side of the base is 756 feet, and the height is 481 feet. So, we can find that the ratio of the base to height is 756/481=1.5717. Euclid , the Greek mathematician wrote the Elements which is a collection of 13 books. In Book 6, Proposition 30, Euclid shows how to divide a line in mean and extreme ratio which we would call " finding the golden section point on the line. " Euclid used this phrase to mean the ratio of the smaller part of the line, to the larger part is the SAME as the ratio of the larger part, to the whole line. Euclid in Elements called dividing a line at the ratio 0.6180399.. : 1 , dividing a line in the extreme and mean ratio . This later gave rise to the name golden mean, golden ratio and even the divine proportion.
Plato , the Greek philosopher theorized about the Golden Ratio. He believed that if a line were divided into two unequal segments so that the smaller segment was related to the larger in the same way that the larger segment was related to the whole, what would result would be a special proportional relationship. that is, a + b a = a b , where a + b is the length of the line, then these ratios are called the Golden ratio. Luca Pacioli wrote a book called De Divina Proportione (The Divine Proportion) in 1509. It contains drawings made by Leonardo da Vinci of the 5 Platonic solids.

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