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How to Draw a Fibonacci Spiral

Updated February 21, 2017

The Fibonacci spiral is a beautiful form found in nature, such as the spiral of a nautilus shell and the centre of sunflowers. A Fibonacci spiral follows a geometric pattern composed of the Fibonacci code. Squares following the dimensions of the Fibonacci code are used to construct such a spiral.

Draw a square that is 1 by 1 unit in measure and a square right next to it with the same dimensions. If using graph paper, quarter inch units work well. Draw a square that is 2 by 2 units below the first two squares. The Fibonacci sequence starts with 0 and 1 and each following number is the sum of the two previous ones. So the sequence goes, 1, 2, 3, 5, 8, 13, 21 and on. This is how we know how to make the squares the correct unit sizes.

Draw a square that is 3 by 3 units to the right of all the previous squares.

Draw a square that is 5 by 5 units above all the previous squares.

Draw a square that is 8 by 8 units to the left of all the previous squares.

Draw a square that is 13 by 13 units below all of the squares and then a 21 by 21 unit square to the right of all of those.

Start with your pencil in the first square you drew which is now in the centre. Draw curving quarter circles through the corners of the squares starting with the centre going counter clockwise and work your way out to the biggest square. These quarter circles should work together to complete a spiral by arching through two diagonal corners of each square. See the drawing for an example. Trace the spiral with a dark pen or marker.

Things You'll Need

  • Paper
  • Pencil
  • Eraser
  • Ruler
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