10.5 The snowflake curve is obtained as follows from an equilateral triangle with sides of length 1: in Step 1, each side is divided into three equal parts; an equilateral triangle is constructed on the middle part; the middle part is then deleted, as in the figure below. In Step 2, Step 1 is repeated for each side of the resulting polygon, and so forth. The snowflake curve results from repeating those steps indefinitely. 1. 2. 3.
10.5 The snowflake curve is obtained as follows from an equilateral triangle with sides of length 1: in Step 1, each side is divided into three equal parts; an equilateral triangle is constructed on the middle part; the middle part is then deleted, as in the figure below. In Step 2, Step 1 is repeated for each side of the resulting polygon, and so forth. The snowflake curve results from repeating those steps indefinitely. 1. 2. 3.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:10.5 The snowflake curve is obtained as follows from an equilateral triangle with sides
of length 1: in Step 1, each side is divided into three equal parts; an equilateral triangle
is constructed on the middle part; the middle part is then deleted, as in the figure below.
In Step 2, Step 1 is repeated for each side of the resulting polygon, and so forth. The
snowflake curve results from repeating those steps indefinitely.
1.
3.
2.
Transcribed Image Text:1. Let sn, In, and p, denote the number of sides, the length of each side, and the
total length of the curve obtained after Step n in the construction, respectively.
Find formulas for sn, In, and hence pn.
2. What is the limit of the length p, of the curve as n → 0?
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