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.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 10AEXP
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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: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.
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?
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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