Helga von Koch’s snowflake curve Helga von Koch's snow- flake is a curve of infinite length that encloses a region of finite area. To see why this is so, suppose the curve is generated by starting with an equilateral triangle whose sides have length 1. a. Find the length L, of the nth curve C, and show that lim,-00 Ln = . = ∞. b. Find the area A, of the region enclosed by C, and show that lim, 00 A, = (8/5) A1. C4 C3 C2 C1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 67E
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Helga von Koch’s snowflake curve Helga von Koch's snow-
flake is a curve of infinite length that encloses a region of finite
area. To see why this is so, suppose the curve is generated by
starting with an equilateral triangle whose sides have length 1.
a. Find the length L, of the nth curve C, and show that
lim,-00 Ln = .
= ∞.
b. Find the area A, of the region enclosed by C, and show that
lim, 00 A, =
(8/5) A1.
C4
C3
C2
C1
Transcribed Image Text:Helga von Koch’s snowflake curve Helga von Koch's snow- flake is a curve of infinite length that encloses a region of finite area. To see why this is so, suppose the curve is generated by starting with an equilateral triangle whose sides have length 1. a. Find the length L, of the nth curve C, and show that lim,-00 Ln = . = ∞. b. Find the area A, of the region enclosed by C, and show that lim, 00 A, = (8/5) A1. C4 C3 C2 C1
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