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Students: Apostolescu Ștefania Bulf Alice Tania Istrate Alexandru

The Golden Ratio.The Fibonacci Sequence.

Putting it as simply as we can, the Golden Ratio exists when a line is divided into two parts and the longer part (a) divided by the smaller part (b) is equal to the sum of (a) + (b) divided by (a), which both equal 1.618.

What is the Golden Ratio?

The composition is important for any image to create an aesthetically pleasing photograph. The Golden Ratio can help create a composition that will draw the eyes to the important elements of the photo.

Images: Golden Ratio or Rule of Thirds

Using the Golden Ratio, you split the picture into three unequal sections then use the lines and intersections to compose the picture.

The Fibonacci sequence is one of the most famous formulas in mathematics. Each number in the sequence is the sum of the two numbers that precede it. So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

The Fibonacci Sequence

It's true that the Fibonacci sequence is tightly connected to what's now known as the golden ratio (which is not even a true ratio because it's an irrational number).

The Importance of the Fibonacci Sequence

While this series of numbers from this simple brain teaser may seem inconsequential, it has been rediscovered in an astonishing variety of forms, from branches of advanced mathematics to applications in computer science, statistics, nature, and agile development.

The head of a flower is also subject to Fibonaccian processes. Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns.

Seed heads

Interesting Example of the Golden Ratio in Nature

The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant. This pattern of branching is repeated for each of the new stems.

Tree branches

Interesting Example of the Fibonacci Sequence in Nature