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…asked mathematician Benoit Mandelbrot.
Our math puzzle this month explores a related question.
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Let’s say that the line segment AD is 1 unit long. |
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AB = BC = CD = 1/3 unit. Now let’s remove segment
BC and replace it with two segments BE and EC, each of which
is 1/3 units long. The length of the path ABECD is 4/3 units. |
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Now let’s do this again at a smaller scale: Remove
the middle third of each segment, AB, BE, EC, and CD, and
replace each one with a path that is similar to ABECD. We
will have a path that looks like this: |
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How long is this path? If we continue this process, replacing each
straight segment with a path 4/3 the length of that segment, how
long will our path become?
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