Fibonnacci and harmonious proportions

In which we learn a basic design principle – and get to practise producing rectangles and circular arcs, duplications, moving by selected handles, applying fill and line attributes etc.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…

This series of numbers – each one the sum of the previous two – is named after Fibonacci, an Italian mathematician of the thirteenth century. It creates patterns that appear repeatedly in the natural world: a spiral composed of a sequence of quarter-circle arcs of these radii, for example, closely resembles that of seashells.

Fibonnacci in architecture

So accustomed are our eyes to Fibonnacci patterns in nature, that it affects the way we feel about architectural spaces. Consecutive numbers in the series create rectangles that are very close to the Golden Rectangle (1: 1.618) beloved of artists and architects since the Renaissance era. Spaces of these proportions are said to be inherently more comfortable than those with arbitrary proportions.

Make your own Fibonnacci squares

To harness Fibonnacci numbers in your own work, start with a drawing area set to 1:50, Feet & Inches, and draw a 1 ft. square.

Make a duplicate square that is attached to the top left of the first one.

Resize the duplicate to 2' x 2'

Duplicate the second square, attached to its bottom left corner.

Repeat the process in a cyclical pattern.

Resize each duplicate to the next Fibonnacci size: 5' x 5', 8' x 8', etc.

Repeat until you have a set up to 21' x 21'

Create a new Design Layer, called "Spiral"

To make it easier to trace over the squares without fear of moving them, rename the existing Design Layer "Squares", and create a new Design Layer called "Spiral".

Create a spiral arc within the small square.

Use the Circular Arc in its default mode (centre of circle, drag out a radius, click to start the arc, drag, and click to finish).
NOTE: For best results, preset the Attributes palette to no Fill (so the arc is hollow), and the Line colour to Red, lineweight 0.7 or 1.0

Repeat for the next size square.

… and the one after that...

Continue until the spiral is complete for all the squares.