EXCURSIONS IN MODERN MATH
EXCURSIONS IN MODERN MATH
5th Edition
ISBN: 9781323741559
Author: Tannenbaum
Publisher: PEARSON C
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Chapter 12, Problem 12E

Exercises 9 through 12 refer to a variation of the Koch snowflake called the Koch antisnowflake. The Koch antisnowflake is much like the Koch snowflake, but it is based on a recursive rule that removes equilateral triangles. The recursive replacement rule for the Koch antisnowflake is as follows:

Koch Antisnowflake

Start: Start with a solid seed equilateral triangle [Fig. 12-36(a) ].

Replacement rule: In each step replace any boundary line segment ____ with a Chapter 12, Problem 12E, Exercises 9 through 12 refer to a variation of the Koch snowflake called the Koch antisnowflake. The , example  1 (where the point is always facing toward the interior of the snowflake). [Figures 12-36(b) and (c) show the figures obtained at Steps 1 and 2, respectively.Chapter 12, Problem 12E, Exercises 9 through 12 refer to a variation of the Koch snowflake called the Koch antisnowflake. The , example  2

Assume that the seed triangle of the Koch antisnowflake has area A = 729 . Let R denote the number of triangles subtracted at a particular step, S the area of each subtracted triangle. T the total area subtracted, and Q the area of the shape obtained at a particular step of the construction. Complete the missing entries in Table  12 12 .

Table 1 2 1 2

R S T Q
Start 0 0 0 729
Step 1 3 81 243 486
Step 2 12 9 108 378
Step 3
Step 4
Step 5
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Chapter 12 Solutions

EXCURSIONS IN MODERN MATH

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