1. 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

2. THE GOLDEN RATIO: FLOWERS

3. 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.

4. 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.

5. 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.

6. Created by: Araldi Nicole Boni Nicolò Cantarelli Matilde TiadlaYouness

7. THE GOLDEN RATIO: SHELLS

8. The unique properties of the Golden Rectangle provides another example. This shape, a rectangle, in which the ratio of the sides a/b is equal to the golden mean (phi), can result in a nesting process that can be 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.

9. Created by: Giorgia Saccani Christian Simonazzi Matteo Falchi Arber Mahilai

10. Created by: Giorgia Saccani Christian Simonazzi Matteo Falchi Arber Mahilai THE END GOLDEN RATIO IN NATURE:BEES THE GOLDEN RATIO: BEES

11. 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.

12. 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.

13. GREAT-GRANDPARENTS In 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.

14. CREATED BY: STACY ARTHUR IVY BOATENG OMAIMA NAJEM MATTEO FLISI

16. HAND FINGERS 1) HAND FINGERS LET’S START WITH SOMETHING SIMPLE. TAKE YOUR HAND AND LOOK AT THE PROPORTIONS OF YOUR INDEX FINGER.

17. 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.

18. 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.

19. 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.

20. CREATED BY: BONESI ANDREA Di GIOVANNI RICCARDO MONGILLI SARA MAHMOUDI ASSMA

21. THE GOLDEN RATIO DEBUNKING THE MYTH OF APPLE’S “GOLDEN RATIO”

22. 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.

23. CREATED BY: HAYTEM CHAOUCH ALESSANDRO CELIBERTI REBECCA LANA ACHRAF MATHLOUTHI