Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 11.4, Problem 1E
Interpretation Introduction

Interpretation:

To find the dimension of the von Koch snowflake.

Concept Introduction:

  • The Koch curve starts with a straight line that is divided up into three equal parts. Using the middle segment as a base, an equilateral triangle is created. Finally, the base of the triangle is removed, leaving us with the first iteration of the Koch curve.

  • From the Koch curve comes the Koch Snowflake. Instead of one line, the snowflake begins with an equilateral triangle. The steps in creating the Koch Curve are then repeatedly applied to each side of the equilateral triangle, creating a snowflake shape.

  • The Koch snowflake is an example of a figure that is self-similar, meaning it looks the same on any scale.

  • The formula for the number of sides in the Koch snowflake is: N(ε) = 3(4n).

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Students have asked these similar questions
Construct tables showing the values of alI the Dirichlet characters mod k fork = 8,9, and 10. (please show me result in a table and the equation in mathematical format.)
Example: For what odd primes p is 11 a quadratic residue modulo p? Solution: This is really asking "when is (11 | p) =1?" First, 11 = 3 (mod 4). To use LQR, consider two cases p = 1 or 3 (mod 4): p=1 We have 1 = (11 | p) = (p | 11), so p is a quadratic residue modulo 11. By brute force: 121, 224, 3² = 9, 4² = 5, 5² = 3 (mod 11) so the quadratic residues mod 11 are 1,3,4,5,9. Using CRT for p = 1 (mod 4) & p = 1,3,4,5,9 (mod 11). p = 1 (mod 4) & p = 1 (mod 11 gives p 1 (mod 44). p = 1 (mod 4) & p = 3 (mod 11) gives p25 (mod 44). p = 1 (mod 4) & p = 4 (mod 11) gives p=37 (mod 44). p = 1 (mod 4) & p = 5 (mod 11) gives p 5 (mod 44). p = 1 (mod 4) & p=9 (mod 11) gives p 9 (mod 44). So p =1,5,9,25,37 (mod 44).
how to construct the following same table?
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