The Golden Spiral

The Golden Spiral is based on a series of squares that can be constructed within the golden rectangle
In geometry it is a particular type of logarithmic spiral with growth factor b equal to φ, the golden section.

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To start the construction draw an arc from one corner of the rectangle until it intersects the adjacent side. You then lead a segment perpendicular to the side that was intersected, from the intersection point to the opposite side.

spi_a2.gif (392 byte)

Repeat the process to form another square ...

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.. and so on.

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By drawing arcs with sequences of squares, one can construct the logarithmic spiral known as the Golden Spiral

spi_fibo1.gif (2810 byte)

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