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Back to Beauty in Maths

Beauty project

Fibonacci spirals

A tiny adding rule becomes a picture. Predict the next square, change the number of squares, and watch the ratios settle.

Careful note: this is a beautiful mathematical construction, not a claim that every spiral in nature is Fibonacci.
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Ratio graph

Can you estimate where the ratios settle?

1.001.251.501.752.001/12/13/25/38/513/821/13ratio value

The ratios jump above and below. Before revealing phi, ask students what horizontal value the points seem to be approaching.

Each new side length is the sum of the previous two.

The spiral is made from quarter-circle arcs.

The ratios move towards the golden ratio.

Connected ideas

This page is part of a wider map.

Open the idea graph