Index

Serial no. chapter

1| Introduction|

2| History|

3| In nature|

4| In human body|

5| In architecture|

6| In art|

7| In day to day life|

8| SIGNIFICANCE|

ACKNOWLEDGEMENT

I would like to express my special thanks of gratitude to my teacher sonali durgam on the topic golden ratio, which also helped me in doing a lot of Research and I came to know about so many new things. I am really thankful to her.

Secondly I would also like to thank my parents and friends who helped me a lot in finishing this project’s information finding work.

I am making this project not only for marks but to also increase my knowledge. THANKS AGAIN TO ALL WHO HELPED ME

Introduction

The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric figures such as the pentagon, pentagram, decagon and dodecahedron. It is denoted , or sometimes . The designations "phi" (for the golden ratio conjugate ) and "Phi" (for the larger quantity ) are sometimes also used (Knott), although this usage is not necessarily recommended. The term "golden section" (in German, goldener Schnitt or der goldene Schnitt) seems to first have been used by Martin Ohm in the 1835 2nd edition of his textbook Die Reine Elementar-Mathematik (Livio 2002, p. 6). The first known use of this term in English is in James Sulley's 1875 article on aesthetics in the 9th edition of the Encyclopedia Britannica. The symbol ("phi") was apparently first used by Mark Barr at the beginning of the 20th century in commemoration of the Greek sculptor Phidias (ca. 490-430 BC), who a number of art historians claim made extensive use of the golden ratio in his works (Livio 2002, pp. 5-6). Similarly, the alternate notation is an abbreviation of the Greek tome, meaning "to cut." In the Season 1 episode "Sabotage" (2005) of the television crime drama NUMB3RS, math genius Charlie Eppes mentions that the golden ratio is found in the pyramids of Giza and the Parthenon at Athens. Similarly, the character Robert Langdon in the novel The Da Vinci Code makes similar such statements (Brown 2003, pp. 93-95). However, claims of the significance of the golden ratio appearing prominently in art, architecture, sculpture, anatomy, etc., tend to be greatly exaggerated. has surprising connections with continued fractions and the Euclidean algorithm for computing the greatest common divisor of two integers. History of golden ratio

The golden ratio has fascinated Western intellectuals of diverse interests for at least 2,400 years. According to Mario Livio: Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematicianLeonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The modern history of the golden ratio starts with Luca Pacioli's De divina proportione of 1509, which captured the imagination[citation needed] of artists, architects, scientists, and mystics with the properties, mathematical and otherwise, of the golden ratio. Golden ratio in nature

The eye, fins and tail all fall at golden sections of the length of a dolphin’s body. The dimensions of the dorsal fin are golden sections (yellow and green). The thickness of the dolphin’s tail section corresponds to same golden section of the line from head to tail.

Every key body feature of the angel fish falls at golden sections of its width and length. The nose, tail section, and centers of the fins of the angel fish fall at first (blue) golden sections. The second golden section (yellow) defines the...