THE GOLDEN RATIO: IT’S EASY!

Do you have any problem in understanding the famous Golden Ratio wich troubles young students all over the

world?

A group of Italian students made it easy! They discovered some applications of the Golden Ratio:

HUMAN BODY

TECHNOLOGIES

NATURE

THE GOLDEN RATIO: FLOWERS

The number of petals in a flower consistently follows the Fibonacci sequence.

Famous examples include the lily which has three

petals, buttercurps which have five, the chicory has got 21, the daisy 34,and

so on. Each petal is placed at 0.618034 per turn allowing for the best possible exposure to

sunlight and other factors.

SEED HAEDS

The head of a flowers is also subject to Fibonacci processes.

Typically Fibonacci number are produced at the center, and then migrate towards the outside to fill

all the space.

Sunflowers provide an example of these spiraling patterns.

In some cases, the seed heads are so tightly packed that total number can get quite high as many as 144 or more.

And when counting these spirals, the total tends to match a Fibonacci number. Interestingly, a highly irrational number is required to optimize filling. “Phi” fits the bill rather nicely.

Created by:

Araldi Nicole

Boni Nicolò

Cantarelli Matilde

TiadlaYouness

THE GOLDEN RATIO:SHELLS

The unique properties of the Golden Rectangle provides anotherexample. This shape, a rectangle, in which the ratio of the sides a/b isequal to the golden mean (phi), can result in a nesting process that canbe repeated into infinity – and which takes on the form of a spiral.

It’s called the logarithmic spiral, and it abounds in nature. Snail shells and nautilus shells follow the logarithmic spiral, as does the cochlea of the inner ear. It can also be seen:in the horns of certain goats;in the shape of certain spiders’ webs.

Created by:

• Giorgia Saccani• Christian Simonazzi• Matteo Falchi• Arber Mahilai

Created by:

• Giorgia Saccani• Christian Simonazzi• Matteo Falchi• Arber Mahilai

THE END

GOLDEN RATIO IN NATURE:BEES

THE GOLDEN RATIO: BEES

Bees are very intriguing. A male bee, a drone, hatches

from an unfertilized egg whereas all females hatch from fertilised eggs. That

means males have just one parent, who produced the egg. Females have two parents: the mother that

produced the egg and the father that fertilized it.

Let’s try and work out what are the facts about the female to male ratio. It’s convenient to represent males and female by their usual signs.

Now imagine a single male, who we’ll call Rob. Now Rob ,being a male, has one parent, the queen (a female). We can draw a family tree for this simple parent family.

GREAT-GRANDPARENTSIn the diagram, you can see that

Rob has one parent (the queen), two grantparents(a drone and another queen).

In turn these two grandparents have their own parents, who

are Rob’s great grand parents.You may like to carry up

drawing a few more generation back. Looking at Rob’s family

tree, count the number of bees in each generation.

Start with the original bee, Rob. He has 1 parent. He has 2 grandparents, then 3 great grandparents, and, going on with our drawing, there willl be 5 great greatgrandparents, 8 great great grandparents,13 great great great grandparents, 21 great great great great grandparents.

The murder victim’s Fibonacci numbers have reappeared!

1 2 3 5 8 13 21.

CREATED BY:STACY ARTHUR

IVY BOATENG

OMAIMA NAJEM

MATTEO FLISI

1) HAND FINGERSHAND FINGERSLETLET’’S START WITH S START WITH

SOMETHING SIMPLE. TAKE SOMETHING SIMPLE. TAKE YOUR HAND AND LOOK AT YOUR HAND AND LOOK AT

THE PROPORTIONS OF THE PROPORTIONS OF YOUR INDEX FINGER.YOUR INDEX FINGER.

EACH SECTION OF YOUR INDEX FINGER FROM THE BASE OF THE WRIST, IS LARGER THAN THE PRECEDING ONE BY ABOUT THE FIBONACCI RATIO OF 1.618, ALSO FITTING

THE FIBONACCI NUMBERS 2,3,5 AND 8.

BY THIS SCALE, YOUR FINGERNAIL IS 1 UNIT IN LENGTH.

CURIOUSLY ENOUGH, YOU ALSO HAVE 2 HANDS, EACH WITH 5 FINGERS, AND YOUR

5 FINGERS ARE EACH COMPRISED OF 3. ALL FIBONACCI NUMBERS.

2) THE RATIO OF THE FOREARM TO HAND

OUR HAND CREATES A GOLDEN SECTION IN RELATION TO YOUR ARM, AS THE RATIO OF YOUR FOREARM TO YOUR HAND IS ALSO 1.618, THE DIVINE

PROPORTION.

3) YOUR FEET

THE FOOT HAS SEVERAL PROPORTIONS BASED ON PHI

LINES, INCLUDING:1- THE MIDDLE OF THE ARCH

OF THE FOOT.2- THE WIDEST PART OF THE

FOOT.3- THE BASE OF THE TOE LINE

AND BIG TOE.4- THE TOP OF THE TOE LINE

AND BASE OF THE “INDEX” TOE.

CREATED BY:BONESI ANDREA

Di GIOVANNI RICCARDOMONGILLI SARA

MAHMOUDI ASSMA

THE GOLDEN RATIO

DEBUNKING THE MYTH OF APPLE’S “GOLDEN RATIO”

The ratio leads to aesthetically pleasing shapes

Market productors use strategies to lead people to buy . For example , the great and famous Apple factory in 1980s invented the Apple logo making people believe that the Apple was based on golden ratio.

But recently, David Cole, product designer at Quora, posted an epic debunking of the Golden Ratio as the impetus of Apple’s own logo.

For example the credit card is a golden rectangle.

CREATED BY:

HAYTEM CHAOUCH

ALESSANDRO CELIBERTI

REBECCA LANA

ACHRAF MATHLOUTHI