Excursions in Modern Mathematics (9th Edition)
Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Chapter 12, Problem 1E

Consider the construction of a Koch snowflake starting with a seed triangle having sides of length 81 cm. Let M denote the number of sides, L the length of each side, and P the perimeter of the "snowflake" obtained at the indicated step of the construction. Complete the missing entries in Table 12-1 Q.

Table 12-1

M L P
Start 3 81 cm 243 cm
Step 1 12 27 cm 324 cm
Step 2
Step 3
Step 4
Step 5
Expert Solution & Answer
Check Mark
To determine

To complete:

The given chart.

Answer to Problem 1E

Solution:

The given chart is,

M L P
Start 3 81cm 243cm
Step 1 12 27cm 324cm
Step 2 48 9cm 432cm
Step 3 192 3cm 576cm
Step 4 768 1cm 768cm
Step 5 3072 13cm 1024cm

Explanation of Solution

Given:

The given chart is,

M L P
Start 3 81 cm 243 cm
Step 1 12 27 cm 324 cm
Step 2
Step 3
Step 4
Step 5

Calculation:

Draw an equilateral triangle with side length of 81cm. The below figure shows the equilateral triangle.

Excursions in Modern Mathematics (9th Edition), Chapter 12, Problem 1E , additional homework tip  1

Figure-1

To the middle third of each of the sides of this seed, add an equilateral triangle with sides of length 27 cm. The result is a 12 sided snowflake with perimeter,

12×27=342cm

Excursions in Modern Mathematics (9th Edition), Chapter 12, Problem 1E , additional homework tip  2

Figure-2

To the middle third of each of the 12 sides of snowflake add an equilateral triangle with sides of length one third of the length of the side. The result is a snowflake with 48 sides each side length of 9 cm and the perimeter is,

48×9=432

Excursions in Modern Mathematics (9th Edition), Chapter 12, Problem 1E , additional homework tip  3

Figure-3

M L P
Start 3 81cm 243cm
Step 1 12 27cm 324cm
Step 2 48 9cm 432cm
Step 3 192 3cm 576cm
Step 4 768 1cm 768cm
Step 5 3072 13cm 1024cm

Therefore, the given chart calculations are stated above.

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Excursions in Modern Mathematics (9th Edition)

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