The Mathematical Study of Mollusk Shells
The logarithmic spiral in Molluskville architecture__________________________.     .    _.   ._____            .                ___________________________________________________ house after fourth renovation If we take coordinates based at the lower right hand corner of the original house, and let a = 1, then the wall holding the original door goes from the corner at (2,1) to the dot at (1,1). After the first renovation, the new wall goes from (2,0) to (2,2). The new red dot comes from rotating the old one 90^{o} counterclockwise about the corner; the new corner comes from rotating the red dot 90^{o} clockwise. Applying this construction to the new red dot and the new corner leads to the red dot and the corner in the second renovation, etc. The red dots are on a logarithmic spiral:

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