INTRO

INTRODUCTIONINTROThe great book of nature can be read only by those who know the language in which it was written. And that language is Mathematics

(Galileo)(1561-1642, Italy)

INTRODUCTIONINTROMathematics

A universal language of the world

INTRODUCTIONINTRO

INTRODUCTIONINTROMathematics rightly viewed possesses not only truth, but supreme beauty

(Bertrand Russell)(1872- 1970, UK)

To apprise the audience about two beautiful aspects of Mathematics, the Fibonacci Numbers & Golden RatioAIM

Fibonacci NumbersFibonacci Numbers in NatureRelationship - Golden Ratio and Fibonacci NumbersGolden Ratio in NatureImpact of Golden Ratio on BeautyUse of Golden Ratio in Contemporary WorldSEQUENCE

FIBONACCI NUMBERS

Leonardo of Pisa (Italy) lived about 1170-1250 and is commonly called Fibonacci. He introduced to Europe a sequence of numbers, what we now call the Fibonacci sequence. However, this sequence was known to Hindustani mathematicians as early as the 6th century.WHO WAS FIBONACCI

FIBONACCI NUMBERS

FIBONACCI NUMBERS

FIBONACCI NUMBERSFIBONACCI NUMBERS

FIBONACCI NUMBERSFIBONACCI NUMBERS

BEES POPULATION GROWTHFIBONACCI NUMBERS

BEES POPULATION GROWTHFIBONACCI NUMBERS

FIBONACCI NUMBERSFIBONACCI NUMBERS - FLOWERS

FIBONACCI NUMBERSFIBONACCI NUMBERS - FLOWERS

FIBONACCI NUMBERSFIBONACCI NUMBERS - FLOWERS

FIBONACCI NUMBERSFIBONACCI NUMBERS - FLOWERS

FIBONACCI NUMBERSFIBONACCI NUMBERS - FLOWERS

FIBONACCI NUMBERSFIBONACCI NUMBERS - FLOWERS

STEM/ BRANCH OF FLOWER/ TREE

STEM/ BRANCH OF FLOWER/ TREE

TreeLeavesTurnsTreeLeavesTurnsElm21Poplar52Cherry32Weeping willow83Almond138Pear83

FIBONACCI NUMBERS - FRUITS

FIBONACCI NUMBERS - FRUITSBananas have 3 or 5 flat sides

FIBONACCI NUMBERS - FRUITS

Note that 5, 8, 13 and 8, 13, 21 are consecutive Fibonacci NumbersFIBONACCI NUMBERS - FRUITS

FIBONACCI NUMBERS

GOLDEN RATIOTwo quantities are in the golden if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller one

GOLDEN RATIO

RELATION BETWEEN GOLDEN RATIO AND FIBONACCI NUMBERSDivide each consecutive Fibonacci NumbersResults gradually converge on the Golden Ratio

Square is greater than itself by one =+ 1 = 2.618 Reciprocal is less than itself by one1/=- 1 = 0.618

UNIQUENESS

A golden rectangle is a rectangle where the ratio of its length to width is the golden ratio. That is whose sides are in the ratio 1:1.618GOLDEN RECTANGLE

GOLDEN RECTANGLE & SPIRAL

GOLDEN RECTANGLE & SPIRAL

GOLDEN RECTANGLE & SPIRAL

GOLDEN RATIO - HUMAN BODY

White line is the bodys heightBlue line, a golden section of the white lineYellow line, a golden section of the blue lineGreen line, a golden section of the yellow linePurple line, a golden section of the green line

GOLDEN RATIO - HUMAN BODY

GOLDEN RATIO - ANIMALS

GOLDEN RATIO - MUSICScale composed of 8 notes,5th and 3rd notes create basic foundationThe closer the design to the Golden Ratio, the better the quality of sound

GOLDEN RATIO - ART & BEAUTY

GOLDEN RATIO - ART & BEAUTY

GOLDEN RATIO - ART & BEAUTY

In 2012 contest to find Britains Perfect Face Most perfect makeup-free faceDrew entries from 8,045 contestants18 years oldstudent from Kent, selected as winnerIMPACT OF GOLDEN RATIO ON BEAUTY

GOLDEN RATIO IN ARCHITECTURE

GOLDEN RATIO IN ARCHITECTURE

GOLDEN RATIO IN GEOMETRY

GOLDEN RATIO IN GEOMETRY

GOLDEN RATIO IN GEOMETRY

ASTON MARTIN AND GOLDEN RATIOAston Martin DB9Aston Martin Rapide S

LOGOS

LOGOS

LOGOS

LOGOS

LOGOSAPPLE IOS 7 NEW ICON SET WITH GOLDEN RATIO OVERLAY

LOGOS

LOGOS

LOGOS/ SIGNATURESBarack Obamas signature and Walt Disneys logo

FASHION / PRODUCTS

CONCLUSION

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