2. Zoning Laws in Molluskville
To start understanding the mathematical problem a snail faces, imagine that you are a citizen of Molluskville, a Flatland community with very strict zoning laws.
______. | | | | |____________| The Model House
Of course if you keep on growing you will have to renovate again and again ...
__________________________. | | | | . | | | |_.| | | .___|__| | | | | | | | | | | | . | | | | | | | | | | | | | | | |___________________________________________________| house after fourth renovation
The red dots at the inside edge of each doorway lie on a logarithmic spiral, as can be straightforwardly calculated.
Our rectangular model is simpler than any actual mollusk shell, but it faithfully illustrates the kind of constraints that shape mollusk shell morphology and the way that these constraints force the appearance of the logarithmic spiral.
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These web essays are designed for those who have already discovered the joys of mathematics as well as for those who may be uncomfortable with mathematics.
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