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# The Golden Ratio and Fibonacci Numbers

This Prezi describes the Golden Ratio/Fibonacci Numbers, their relationship, and where you find them in life.
by

## Govind Ramesh

on 15 April 2014

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#### Transcript of The Golden Ratio and Fibonacci Numbers

Fibonacci Numbers can be found in the way tree trunks grow, the petals or seeds on a flower, or the leafs on a palm tree. On pinecones and pineapples, if you look from the top, there are spirals. The spirals are usually a Fibonacci Number of 8 or 5 in clockwise and counterclockwise spirals. There are 3 sections on a banana, and 5 sections in an apple. On a flower, you can count the outer petals, the inner petals, the stamens, the carpel, and the sepal. Here are some flowers that use Fibonacci Numbers:
Lily, Iris-3 petals
Buttercup,wild rose,columbine,lark spur-5 petals
Delphiniums-8 petals
Ragwort,corn marigold,cineraria-13 petals
Aster,black-eyed susan-21 petals
Plantain,pyrethrum-34 petals
Michaelmas daisy,astercae-55 petals
Astercae-89 petals
On the back of a
passiflora incarnate
there are 3 sepals, 5 outer petals, 5 inner petals, 5 stamens, and 3 carpels. Have you ever wondered why some objects are so pleasing to your eye? These objects probably have the Golden Ratio or Fibonacci Numbers. Evidence shows that objects with these requirements are pleasing to the eye. Plants use Fibonacci Numbers so they can get as many seeds as possible into the seedhead, to get more sunlight for each leaf, and maximize the space each leaf gets. If you look around you at nature, you will find tons of things with Fibonacci Numbers.
What Is the Golden Ratio

The Golden Ratio is an irrational number with the value of about 1.618.The Golden ratio is also known as the Divine Ratio, The Golden Mean, and the Golden Section. It has always existed in the universe. The sign for the Golden Ratio is the Greek letter phi. The Golden Ratio was first understood by ancient mathematicians in Egypt. You can find the Golden Ratio in everyday life, from a skyscraper to a Nautilus shell. The Golden Ratio derived from the golden rectangle. The golden rectangle has a side ratio of the Golden Ratio. The golden rectangle is used in paintings, architecture and buildings.

What Are Fibonacci Numbers

The Fibonacci numbers are named after Leonardo Fibonacci “Bigollo” Pisano. The Fibonacci numbers are an irrational sequence of integers. It starts with one where you take the latter and the former number, and add them to get the next number.

Fibonacci Numbers in Plants
Relationship Between the Golden Ratio and Fibonacci Numbers
You can find the relationship of the Golden Ratio and Fibonacci Numbers, by taking the latter number from the Fibonacci sequence, and dividing it by the former number.This will form a ratio. As the ratios devolop, it will become closer to the Golden Ratio. Even though it seems like the ratios are the Golden Ratio, the ratios will never reach the Golden Ratio exactly.
Fibonacci Numbers in Art
There are quite a few Golden Rectangles in art. In The Vitruvian Man, there are 3 major Golden Rectangles. One for the head, one for the torso and one for the legs. In Mona Lisa, her face is a perfect Golden Rectangle. There are lots of Golden Rectangles in The Last Supper. There are 3 Rectangles where the people sit, 3 above, and 3 below the people. There are lots of Golden Rectangles in art.
The Golden Ratio
and
Fibonacci Numbers

Fibonacci Numbers in Humans
You can find lots of Fibonacci Numbers in your body. On your face, you have 2 eyes, 2 ears, 2 nostrils, 1 nose, 2 lips, 1 mouth, and 1 neck. You have 2 arms , and on your arms, you have 2 hands, 8 fingers, 2 thumbs, 3 sections on each arm and finger, and 2 sections on each thumb. Also, the space between your elbow and your wrist makes a perfect Golden Rectangle. We have the same on our legs as on your arm. Inside your body, you have 2 livers, 1 brain, 1 skull, 1 stomach, and 1 heart. As you can see, there are not just Fibonacci Numbers in nature. It's also there in humans.

Using Fibonacci Numbers
to Help in Life
13 year old Aidan Dwyer created a solar panel tree using his knowledge of the Fibonacci numbers. He found a specific way trees branch using Fibonacci Numbers so they get more sunlight and live longer. Aidan made his tree, but using solar panels. This tree is more effective in getting energy than solar panels in an array, because each panel gets more sunlight. If more people use the Fibonacci Numbers and the Golden Ratio, the world will be a better place.

Leonardo Fibonacci Pisano was born in 1175 at Pisa, Italy. His nickname was “Bigollo,” meaning traveler. As a teenager, Fibonacci traveled with his dad. On one of his travels, he was introduced to the Hindu-Arabic system of numbers (What we use today). Fibonacci didn’t actually invent the Fibonacci sequence. Fibonacci numbers were originated in India. Fibonacci only brought the numbers to Europe. Fibonacci did however use these numbers in his book Liber Abaci. Fibonacci died in the year 1250.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34
These are the Fibonacci Numbers
This is the Golden Ratio's
sign, Phi given by Mark Barr.
These are Golden Rectangles found on the Statue of Athena
Every ten floors on the UN building is a Golden Rectangle
Fibonacci Numbers in Architecture
There are multiple ways to find the Golden Ratio in architecture. The Statue of Athena in Greece, has a Golden Rectangle from the forehead to the chin, and another one from the nostril to the earlobe to the chin. In the
Parthenon, from the bottom of the roof to the
ground, there is a perfect golden rectangle.
It is also there in the space between the
pillars. You can find Golden Rectangles
every 10 floors on the UN building.
Bibliography
library thinkquest.org/trio/TTQ05063/fnhistory.htm
www.barcodesinc.com/articles/fibonacci-numbers.htm
library thinkquest.org/27890/mainIndex.html
www.goldennumber.net/golden-ratio-history/
http://www.treehugger.com/clean-technology/13-year-old-makes-a-solar-breakthrough-with-fibonacci-sequence.html
lily
delphinium
asteraceae
cineraria
plantain
Full transcript