TEST BANK FOR Chaotic Dynamics_ An Introduction Based on Classical Mechanics By Tamás Tél, Márton Gruiz Converted

Solution 2.2 Let the area of the largest regular triangle inscribed into the island be A0, which is also the area in the zeroth step of the Koch construction. In the first step, three smaller triangles are added, with an area of A0/9 each. In the nth step, the number of new triangles of area A0/9n is 3 × 4n−1. The total area of all the small triangles is therefore A0 ∞ n=1 3 × 4n−19−n = A0/3 ∞ n=0(4/9)n . This is a geometrical series of quotient 4/9. Thus, the area increme...