Fractals

1
Fractals Lesson 4

• The perimeter and area of the Von Koch Snowflake

2
Learning objectives

• We are learning to
• Understand the difference between term-to-term
  rules and position-to-term rules.
• Write an expression to describe the nth term of a
  sequence.

3
Learning outcome

• By the end of the lesson you will
• Understand the difference between term-to-term
  and position-to-term rules.
• Have derived the position-to-term rule for the
  number of edges and the length of each edge of
  the Von Koch Snowflake.
• Have made a discovery about the curious
  properties of the Von Koch snowflake.

4
Lesson 4 - Overview

• Patterns in sequences
• Position-to-term rules of the Von Koch Snowflake
• A curious property!
• Thinking about our learning!
• Displays and narration

5
1. Patterns in sequences

• 1, 2, 4, 8,
• Term to term rule

6
1. Patterns in sequences

• 10, 13, 16, 19
• Term to term rule

7
1. Patterns in sequences

• Term to term rule
• multiply by ½

8
2. The Von Koch Snowflake
Pattern Number Number of edges Number of edges Length of each edge Length of each edge Total Perimeter Total Perimeter
1 3 9 27
2 12 3 36
3 48 1 48
4 192 1/3 64
5 768 1/9 85 1/3

9
2. Von Koch Snowflake
Pattern Number Number of edges Number of edges Length of each edge Length of each edge
1 3 9
2 12 3
3 48 1
4 192 1/3
5 768 1/9
10
10
2. Von Koch Snowflake
11
Nth terms

• Number of edges sequence
• 3, 12, 48, 192, 3 x 4n-1
• Length of each edge sequence
• 9, 3, 1, 1/3, 9 3n-1

12
Sequence showing the length of the perimeter 27,
36, 48, 64,
13
What is the perimeter of pattern number 6?
14
(No Transcript)
15
Learning outcome

• By the end of the lesson you will
• Understand the difference between term-to-term
  and position-to-term rules.
• Have derived the position-to-term rule for the
  number of edges and the length of each edge of
  the Von Koch Snowflake.
• Have made a discovery about the curious
  properties of the Von Koch snowflake.