To construct the snowflake curve, start with an equilateral triangle with sides of length 1. Step 1 in the construction is to divide each side into three equal parts, construct an equilateral triangle on the middle part, and then delete the middle part (see the figure). Step 2 is to repeat step 1 for each side of the resulting
(a) Let
(b) Show that
(c) Sum an infinite series to find the area enclosed by the snowflake curve.
Note: Parts (b) and (c) show that the snowflake curve is infinitely long but encloses only a finite area.
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Chapter 11 Solutions
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