Applications of the Fibonacci Sequence
Natural and artificial instances of the Golden Ratio
The Fibonacci Sequence is one of the most famous formulas in the realm of number theory. Even if you are not a mathematics hobbyist, it is likely that you have heard of Fibonacci numbers or the “Golden Ratio” at some point in your life.
The Fibonacci sequence takes top billing primarily because it is so ubiquitous in nature. From the iconic spirals in flower petals to the reproduction rate of a pair of rabbits, this sequence seems to pop up everywhere!
What is the Fibonacci Sequence?
The Fibonacci Sequence is a series of numbers, where each number in the sequence is the sum of the two previous numbers. The sequence starts at 0 and 1, with the sequence continuing as 0, 1, 1, 2, 3, 5, 8, and so on.
Taking n as the index of a given number in the sequence, this pattern can be mathematically described as: Fₙ = Fₙ₋₁ + Fₙ₋₂.
It is important to note that this sequence is not the same as the aforementioned Golden Ratio. However, the two models are very closely related. More accurately, the Golden Ratio refers to the ratio that the Fibonacci sequence approaches as n approaches infinity.
