KIRLOSKAR PNEUMATIC CO. LIMITED A Kirloskar Group Company The Golden ratio (or Divine Proportion) A.M. Bhide, R & E (ACD) 1
KPCL Mission, Vision & Values 2
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
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
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
Famous irrational numbers 6
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. 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
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 2/1 2.00 3/2 1.50 5/3 1.67 8/5 1.60 13/8 1.625 21/13 1.615 34/21 1.619 55/34 1.618 9
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
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
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
What is a Golden ratio / Divine proportion 13
Finding the phi graphically 14
Pentagon and Golden ratio 15
Golden ratio from Geometry Geometric ratios involving : Pentagon 16
Golden ratio and regular polygons Geometric ratios involving : Decagon 17
Spiral Development Nautilus shell 18
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
Tool to check Golden Ratio in Designs 20
Golden ratio / Divine proportion and Architecture 21
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 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
Golden ratio & Product Design 24
Application of Golden ratio in Logo-design 25
Application of Golden ratio in Logo-design National Geographic British Petroleum 26
Application of Golden ratio in Logo-design 27
Application of Golden ratio in Jewelry 28
Nature loves Golden ratio Good proportion is an important element of beauty as seen in these pictures 29
Plant Growth and Fibonacci 30
Flowers : No of Petals in Flowers 1 2 3 5 8 13 21 34 1, 2, 3, 5, 8, 13, 21,34 31
Flowers : Blooming sequence 32
Sunflower, Spirals and Fibonacci series Seed Pattern 13 anticlockwise spirals and 21 clockwise spirals 33
Sunflower, Spirals and Fibonacci series 34
Pineapple spirals & Fibonacci sequence. 3 spirals in pineapple cone which are 3 adjacent numbers in Fibonacci series / sequence 5,8, and 13 35
Galaxy spirals & Fibonacci sequence. 36
Sea Wave spirals & Fibonacci Numbers 37
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
Compressor sizes and Golden ratio Compressor Model LP Size (mm) HP size (mm) Reciprocating compressor Ratio of LP / HP BTD-RM 470 290 1.621 BTD-QM 385 235 1.638 BTD-PM 355 215 1.651 BTD-JM 316 194 1.628 BTD-LM / MM 255 160 1.594 BTD-NM 194 130 1.492 Screw compressor 2 stage K-300 (KPC) 204 127 1.606 K-325 (SRM) 231 165 1.400 39
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 -- -- 1000 1600 600 1.600 A 1200 1500 2600 1100 1.733 A 2100 2400 4200 1800 1.750 A 3500 4500 9000 4500 2.000 A 7000 8000 14400 6400 1.800 A 7500 550 1600 1050 2.909 TA-2000 600 1900 1300 3.167 TA-2020 2000 4000 2000 2.000 TA-3000 4000 8000 4000 2.000 TA-6000 6600 11800 5200 1.788 TA-9000 1225 1750 525 1.429 C-250 1925 2625 700 1.364 C-350 1575 2275 700 1.444 C-400 2100 4200 2100 2.000 C-700 4200 6400 2200 1.524 C-950 4500 7500 3000 1.667 C-1000 900 2090 1190 2.322 P-300 1600 3350 1750 2.094 P-400 2600 4500 1900 1.731 P-500 4000 6500 2500 1.625 P-600 6000 11500 5500 1.917 P-700 2566 4200 1634 1.637 ZHC-7000 3966 6416 2450 1.618 ZHC-10000 6242 9917 3675 1.589 ZHC-15000 1400 3400 2000 2.429 TMC 2600 4900 2300 1.885 TMB 4000 8100 4100 2.025 TMA 40
Compressor Impeller sizes & Golden ratio A-3500 CN Design D1 D2 Stage D1 (mm) D2 (mm) Ratio 1 143.8 243.7 1.695 2 105.0 191.4 1.828 3 69.6 134.4 1.931 41
Paper sizes do not follow Golden ratio Paper Size Length Width Ratio A4 297 mm 210 mm 1.4142 B4 353 mm 250 mm 1.4142 Legal 355 mm 216 mm 1.6435 Ledger 17 11 1.5454 Letter 11 8.5 1.2941 42
Application Playing & business of Golden cards ratio - in Ratios Logo-design Playing cards Length (mm) Width (mm) Ratio Standard 88.9 57.1 1.53 Poker 88.9 63.5 1.40 Business Cards USA / Canada 88.9 50.8 1.75 KPCL 92.0 52.0 1.77 43
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 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
Suggested Reading web sites 1. http://www.world-mysteries.com/sci_17.htm 2. http://www.banskt.com/blog/golden-ratio-in-logodesigns/ 3. http://www.maths.surrey.ac.uk/hostedsites/r.knott/fibonacci/fib.html 4. http://www.goldennumber.net/golden-ratio/ 5. http://jwilson.coe.uga.edu/emat6680/parveen/gr_in_ art.htm 6. http://www.goldenmeangauge.co.uk/fibonacci.htm 46
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
KIRLOSKAR PNEUMATIC CO. LIMITED A Kirloskar Group Company www.kirloskarkpcl.com 48