Harvard University,FAS
Fall 2003

Mathematics Math21b
Fall 2003

Linear Algebra and Differential Equations

Course Head: Oliver knill
Office: SciCtr 434
Email: knill@math.harvard.edu

The Dimension of the Massachusetts Coastline

(An example of a data fitting problem)
The number of squares of length 1/n needed to cover the circle grows linearly with n. The circle has dimension 1. The number of squares of length 1/n needed to cover the dis grows like n2. The disk has dimension 2.


On the other hand, the number of squares of length 1/n needed to cover the coast of Massachusetts grows like nd with a number d between 1 and 2. The curve appears to be a fractal. The measurement of the number of squares is a counting exercice. The computation of the growth rate needs a linear fit. ( More Details (PDF))


PDF File with information
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