On the left is a summary of the data so far, and an extrapolation. On the right is a graph of Ln vs n. | |||||||||||||||||||||||||||||||
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The length of the Koch curve is greater than each Ln, so greater than every number. That is, the Koch curve has infinite length. | |||||||||||||||||||||||||||||||
Here's an interesting corollary to the infinite length of the Koch curve. | |||||||||||||||||||||||||||||||
    Not only does the Koch curve itself have infinite length, but measured along the curve, the length of any pair of points in the Koch curve is infinite. | |||||||||||||||||||||||||||||||
Do you see why? | |||||||||||||||||||||||||||||||
To make these computations concrete, note that if the original L0 is 1 meter, then | |||||||||||||||||||||||||||||||
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Yet both have a horizontal extent of only one meter. |
Return to Ineffective Ways to Measure.