The Golden Spiral

The construction of the golden spiral

The Golden Spiral, also known as the Golden Spiral or Fibonacci Spiral, is a geometric shape based on the Fibonacci sequence that is often found in nature and art. The Fibonacci sequence is a series of numbers in which each number is the sum of the two preceding numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. The Golden Spiral is created by drawing a series of squares with sides given by the numbers of the Fibonacci sequence, and then drawing a curve that connects the opposite corners of the squares. This curve, when drawn correctly, forms a spiral that gets closer and closer to the shape of the Golden Spiral as it moves towards infinity.

The golden spiral is fascinating because it appears in various natural phenomena and is often considered aesthetically pleasing. It is found in the shapes of galaxies, hurricanes, seashells, and even the proportions of the human body. Its mathematical properties make it a subject of interest in fields such as art, architecture, and design.

To build a Golden Spiral, follow these steps:

1. Draw a square with a side length of 1 unit.
2. Next to this square, draw another square with a side length of 1 unit.
3. Connect the opposite side of the two squares you just drew with a rounded curve.
4. Draw a third square, with a side length equal to the sum of the lengths of the two previous squares (1+1=2).
5. Continue this process, adding squares with sides of successive lengths of the Fibonacci sequence (1, 2, 3, 5, 8, etc.) and connecting the opposite corners of each square with a rounded curve.
6. Continue as long as desired, obtaining a spiral that is ever closer to the shape of the Golden Spiral.

This is just one method of constructing the Golden Spiral, but there are several other techniques that can be used to achieve similar results.

The construction created can be related to the Fibonacci numbers using the construction indicated on the side.