The Golden ratio (or Divine Proportion)

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1 KIRLOSKAR PNEUMATIC CO. LIMITED A Kirloskar Group Company The Golden ratio (or Divine Proportion) A.M. Bhide, R & E (ACD) 1

2 KPCL Mission, Vision & Values 2

3 Outline of presentation What is a Golden ratio Fibonacci series Relation between Golden ratio and Fibonacci number Golden ratio in Architecture Golden ratio in Human Body Golden ratio in product and Logo design Golden ratio and Plants / Flowers / Fruits Golden ratio in Engineering (just a thought) Suggested readings (web sites / Books) 3

4 What is a Golden ratio / Divine proportion Things with the Golden Ratio / Divine proportion are visually appealing An irrational number, approximately 1.618, with special properties. The reciprocal of the Golden Ratio has the same decimal integers (1/1.618 = 0.618) x (1/ ) = 1 as well as - (1/ ) = 1 Found in nature (Plants and animals), art, and architecture. 4

5 What is a Golden ratio / Divine proportion We work with many important irrational numbers in Mathematics viz. pi, e, 2. Since we don't want to make the Golden Ratio feel left out, we will give it its own Greek letter: phi. Other Names : golden section, golden mean, golden number, divine proportion, divine section and golden proportion. Φ φ Phi 5

6 Famous irrational numbers 6

7 What is a Golden ratio / Divine proportion Well, before we answer that question, let's examine an interesting sequence (or list) of numbers. Actually the series starts with 0, 1 but to make it easier we ll just start with: 1, 1 7

What is a Golden ratio / Divine proportion To get the next number we add the previous two numbers together. So now our sequence becomes 1, 1, 2. The next number will be 3.

8 What is a Golden ratio / Divine proportion To get the next number we add the previous two numbers together. So now our sequence becomes 1, 1, 2. The next number will be 3. So the next number should be 2+3, or 5. Here is what our sequence should look like if we continue on in this fashion for a while: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377,. 8

9 Fibonacci Sequence & the Golden Ratio The series becomes 1,1,2,3,5,8,13,21,34,55 This is actually the Fibonacci series. Have a closer look at the ratios between successive numbers. As you continue, the number gets closer to the golden ratio 2/ / / / / / / /

10 Who was Fibonacci? Who Was Fibonacci? 1. Born in Pisa, Italy in 1175 AD 2. Full name was Leonardo Pisano 3. Traveled extensively around the Mediterranean coast and learned systems of arithmetic 4. Realized the advantages of the Hindu- Arabic system. Fibonacci Day : Fibonacci Day is November 23rd, as it has the digits "1, 1, 2, 3" which is part of the Fibonacci sequence. 10

11 Let us ask oneself a question Look at the following rectangle Now ask yourself, which of them seems to be the most naturally attractive rectangle? If you said the first one, then you are probably the type of person who likes everything to be symmetrical. Most people tend to think that the third rectangle is the most appealing. 11

12 The natural choice is third rectangle Have you figured out why the third rectangle is the most appealing? That's right - because the ratio of its length to its width is the Golden Ratio! For centuries, designers of art and architecture have recognized the significance of the Golden Ratio in their work. 12

13 What is a Golden ratio / Divine proportion 13

14 Finding the phi graphically 14

15 Pentagon and Golden ratio 15

16 Golden ratio from Geometry Geometric ratios involving : Pentagon 16

17 Golden ratio and regular polygons Geometric ratios involving : Decagon 17

18 Spiral Development Nautilus shell 18

19 Where can we use Golden ratio? Other areas of application of Golden ratio Stock market analysis Art composition and design Music Product Design (Aesthetics) Logo Design Fashion Design A lot more.. 19

20 Tool to check Golden Ratio in Designs 20

21 Golden ratio / Divine proportion and Architecture 21

22 Golden ratio and Human Body 22

Golden ratio & Music There are 13 keys divided into 8 white and 5 black keys 5 black keys are split into 2 and 3 All the above numbers are members of Fibonacci

23 Golden ratio & Music There are 13 keys divided into 8 white and 5 black keys 5 black keys are split into 2 and 3 All the above numbers are members of Fibonacci series It is believed that Mozart (who is one of the greatest Western classical music composer, used Fibonacci series in his compositions to create Symphony and Harmony. 23

24 Golden ratio & Product Design 24

25 Application of Golden ratio in Logo-design 25

26 Application of Golden ratio in Logo-design National Geographic British Petroleum 26

27 Application of Golden ratio in Logo-design 27

28 Application of Golden ratio in Jewelry 28

29 Nature loves Golden ratio Good proportion is an important element of beauty as seen in these pictures 29

30 Plant Growth and Fibonacci 30

31 Flowers : No of Petals in Flowers , 2, 3, 5, 8, 13, 21,34 31

32 Flowers : Blooming sequence 32

33 Sunflower, Spirals and Fibonacci series Seed Pattern 13 anticlockwise spirals and 21 clockwise spirals 33

34 Sunflower, Spirals and Fibonacci series 34

35 Pineapple spirals & Fibonacci sequence. 3 spirals in pineapple cone which are 3 adjacent numbers in Fibonacci series / sequence 5,8, and 13 35

36 Galaxy spirals & Fibonacci sequence. 36

37 Sea Wave spirals & Fibonacci Numbers 37

38 Application of Golden ratio in Engineering Cylinder sizes reciprocating Screw rotor sizes in 2-stage screw compressors Length to width ratio of foot print Capacity Range definitions Drawing paper sizes Screens of Control panels Overall dimensions of Control Panels KPCL Brand Logo Items in day-today life 38

39 Compressor sizes and Golden ratio Compressor Model LP Size (mm) HP size (mm) Reciprocating compressor Ratio of LP / HP BTD-RM BTD-QM BTD-PM BTD-JM BTD-LM / MM BTD-NM Screw compressor 2 stage K-300 (KPC) K-325 (SRM)

40 Compressor Frame Range & Golden ratio Manufacturer Kirloskar Cameron Ingersoll Rand FS - Elliot Atlas Copco Samsung Minimum Flow Maximum flow Range Ratio max flow to min flow Model CFM CFM CFM A A A A A TA TA TA TA TA C C C C C C P P P P P ZHC ZHC ZHC TMC TMB TMA 40

41 Compressor Impeller sizes & Golden ratio A-3500 CN Design D1 D2 Stage D1 (mm) D2 (mm) Ratio

Paper sizes do not follow Golden ratio Paper Size Length Width Ratio A4 297 mm 210 mm 1.

42 Paper sizes do not follow Golden ratio Paper Size Length Width Ratio A4 297 mm 210 mm B4 353 mm 250 mm Legal 355 mm 216 mm Ledger Letter

43 Application Playing & business of Golden cards ratio - in Ratios Logo-design Playing cards Length (mm) Width (mm) Ratio Standard Poker Business Cards USA / Canada KPCL

44 Golden ratio and Kirloskar Logo 44

Summary Nature loves to have Golden ratio in it's construction evident from lost of examples The visual designers, who apply aesthetics principles use golden ratio into

45 Summary Nature loves to have Golden ratio in it's construction evident from lost of examples The visual designers, who apply aesthetics principles use golden ratio into considerations In engineering products, the golden ratio has little significance and not so evident. Designers can consider golden ratio as one of the guiding principle for product design. 45

46 Suggested Reading web sites art.htm

47 Suggested Reading Books / Thesis 1. The golden ratio and Fibonacci numbers by R. A. Dunlap -World Scientific Publishing Company (1998) 2. The Golden Ratio_ The Story of PHI, the World's Most Astonishing Number- by Mario Livio- Broadway Books (2003) 3. The Divine Proportion by H. E. Huntley (1970) 4. The Fibonacci Sequence Its History, Significance and Manifestation in Nature by Anna Grigas - BS Thesis Liberty University (2013) 47

48 KIRLOSKAR PNEUMATIC CO. LIMITED A Kirloskar Group Company 48

Fibonacci s Mathematical Contributions

Fibonacci s Mathematical Contributions Who Was Fibonacci? ~ Born in Pisa, Italy in 1175 AD ~ Full name was Leonardo Pisano ~ Grew up with a North African education under the Moors ~ Traveled extensively around the Mediterranean coast ~ Met