Fibonacci Spiral
A Fibonacci spiral is a geometric pattern derived from the Fibonacci sequence.
This pattern is created by drawing a series of connected quarter-circles inside a set of squares that have their side according to the Fibonacci sequence. We start the construction of the spiral with a small square, followed by a larger square that is adjacent to the first square. The side of the next square is the sum of the two previous squares, and so on.
Each quarter-circle fits perfectly within the next square in the sequence, creating a spiral pattern that expands outward infinitely.
After studying the Fibonacci spiral we can say that every two consecutive terms of the Fibonacci sequence represent the length and breadth of a rectangle.
Let us now calculate the ratio of every two successive terms of Fibonacci sequence and see the result.
- F2/F1 = 1/1 = 1
- F3/F2 = 2/1 = 2
- F4/F3 = 3/2 = 1.5
- F5/F4 = 5/3 = 1.667
- F6/F5 = 8/5 = 1.6
- F7/F6 = 13/8 = 1.625
- F8/F7 = 21/13 = 1.615
- F9/F8 = 34/21 = 1.619
- F10/F9 = 55/34 = 1.617
- F11/F10 = 89/55 = 1.618 (Golden Ratio)
Thus, we see that for the larger term of the Fibonacci sequence, the ratio of two consecutive terms forms the Golden Ratio.
Note: A Fibonacci spiral is a geometric pattern derived from the Fibonacci sequence.
Fibonacci Sequence: Definition, Formula, List and Examples
Fibonacci sequence is a series of numbers where each number is the sum of the two numbers that come before it. The numbers in the Fibonacci sequence are known as Fibonacci numbers and are usually represented by the symbol Fₙ. Fibonacci sequence numbers start with the following 14 integers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233.
Table of Content
- Fibonacci Sequence
- Fibonacci Sequence Formula
- Fibonacci Spiral
- Golden Ratio to find Fibonacci Sequence
- Golden Ratio Formula
- Fibonacci Series in Pascal’s Triangle
- Fibonacci Sequence Properties
- Fibonacci Sequence Examples
- Practice Problems on Fibonacci Sequence
- Fibonacci Sequence – FAQs
There are various applications of Fibonacci sequence in real life, such as in the growth of trees. As the tree grows, the trunk grows and spirals outward. The branches also follow the Fibonacci sequence, starting with one trunk that splits into two, then one of those branches splits into two, and so on.
Let’s learn about Fibonacci Sequence in detail, including Fibonacci sequence formula, properties, and examples.