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The Fibbonaci Sequence and TV SHOWS:
The Fibonnaci Sequence can be seen in the show: Criminal Minds where a serial killer uses the sequence to choose both the amount of victims at a given time and the location of their hometowns.
Euclid’s Element is what provides the first known written definition of what is now called the golden ratio.
He said: “A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less, that is the Golden Ratio.
You probably realized that if 61.77 divided by 38.22
will give you the same answer as 100 (The total) divided by
61.77 (The longest length). THAT'S THE GOLDEN RATIO!
Arguments on who truly invented the Golden ratio?
Even though the Golden ratio has been used in a vareity of different
structures, no one truly knows who invented the Golden ratio. Many have argued that the Greeks invented it because of the parthenon but many have also suggested that the Egyptians invented it because the golden ratio is also used in their pyramids. Unfortunately there is no significant proof as to who created the golden ratio. All people know is that the first person to write down the formula was Euklides in about 300 bc. He was a Greek mathematician who lived in alexandria.
Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and pentagons. The Greeks usually related the discovery of this concept to Pythagoras or his followers. The regular pentagram, which has a regular pentagon inscribed within it, was the Pythagoreans' symbol
Another great structure was the Parthenon it was perhaps the best example of a mathematical approach architectures. Once its ruined triangular pediment is restored, the ancient temple fits almost precisely into a golden rectangle. The section of the rectangle lines up perfectly with major architectural features of the structure.
This is an a painting
Why the Golden Ratio is important?
How does this relate to art?
Mona-Lisa by Leonardo Da Vinci is an example of how art relates to the Golden Ratio. This picture includes lots of Golden Rectangles. In above figure, we can draw a rectangle whose base extends from the woman's right wrist to her left elbow and extend the rectangle vertically until it reaches the very top of her head. As a result, we will have a golden rectangle. Also, if we draw squares inside this Golden Rectangle, we will discover that the edges of these new squares all come to the important focal points of the woman in the picture (her chin, her eye, her nose, and the upturned corner of her mysterious mouth).
It is believed that Leonardo, as a mathematician tried to add in of mathematics into art. This painting seems to be made firmly lined up with golden rectangle.
How does this relate to Architectures?
Try to identify the places were
the golden ratio was used on the
painting below.
As you can see the golden ratio was used when painting the proportions of the body, Along with the facial aspects (eyes, mouth, etc).
You might not realize it but many buildings in Greece have been built with the golden ratio in mind. The Great Pyramid of Giza is one of the earliest examples of the use of the golden ratio. The length in the base is 756 feet, and the height is 481 feet. So, to find the ratio of the vase to the high, you just divide the two which give you an answer of 1.5717 (756/481)
The Fibonacci sequence is just adding the
two numbers/ elements behind it to get the
next element! (Starts at 1)
How to find the golden ratio
The overall idea of the golden ratio is that the longer length (of any object or line) divide by the smaller length the other part is the same as the whole length divide by the longest length (In the end If both the equations equal 1.6180... You got the golden ratio)
For example:
Try it yourself if A=61.77 and B=38.22
you should get the golden ratio
As you can see, the support towers are placed using the Golden ratio in mind. The golden ratio can also be used, flipped around.
For the Parthenon below. Try to identify the places were the golden ratio is used.
Now for an activity!!!
Try creating a simple masterpiece
using the golden ratio!!
What are the similarities between
Fibonacci's Sequence and
The Golden Ratio/ "phi"?
If you use the numbers in Fibonacci Sequence and divide any number with the number behind it. For example 1 divided by 1, 2 divided by 1and then 3 divided by 2 you will start to see that it's getting closer and closer to the golden ratio.
The relationship between the Golden Ratio and Fibonnaci Sequence can be seen in the above graph. We can see that it approaches the Golden Ratio but never reaches the exact value.
The Fibbonacci sequence is named after Leonardo of Pisa who was well known as Fibonacci. His book: Liber Abaci introduced the sequence to Western European math. It is closely related to the Golden Ratio already described in this presentation.
You will eventually see that your
answer will match the golden ratio
A B B/A
2 3=1.5
3 5=1.666
5 8=1.6
8 13=1.625
....................
144 233=1.618055
It can be further defined as a numerical convention that can be translated into many forms. It has been used in math, architecture, poetry, music, art and even as a system for predicting the growth of the stock market.
This is a painting which was created by Martina Schettina. The painting shows all of the numbers which are involved in the Fibonnaci Sequence.