- #1
Stochastic13
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Homework Statement
Construction begins with an equilateral triangle with sides of length one unit. In the first iteration triangles with length one third are added to each side. Next, triangles of length 1/9 are added to all sides, etc., etc.
Is it possible for a bounded region to have a finite area and infinite perimeter? Explain.
Homework Equations
The Attempt at a Solution
Yes, If each time that iterations are increased the ratio of segment number to length is more than one, then by the geometric series test the series diverges and thus has infinite parameter. Also, if ratio of area is less than 1 as number of iterations goes to infinity, then the area converges by the geometric series test. Does that sound like I answered the question? What can you recommend for a better answer? Thanks.