Question 5 - Relation of Shape Sequences to Number Sequences - Chapter 1 Class 6 - Patterns in Mathematics (Ganit Prakash)

Transcript

Question 5 To get from one shape to the next shape in the Koch Snowflake sequence, one replaces each line segment ‘-’ by a ‘speed bump’ . As one does this more and more times, the changes become tinier and tinier with very very small line segments. How many total line segments are there in each shape of the Koch Snowflake? What is the corresponding number sequence? (The answer is 3, 12, 48, ..., i.e., 3 times Powers of 4; this sequence is not shown in Table 1.) In the Koch Snowflake sequence, the number of line segments in each shape is:​ 1st shape: 3 segments 2nd shape: 12 segments 3rd shape: 48 segments 4th shape: 192 segments 5th shape: 768 segments This forms the sequence: 3, 12, 48, 192, 768, ...​ Which we can write as 3, 3 × 4, 3 × 42, 3 × 43, 3 × 44,… Here, Number of lines = 3 × Powers of 4 Pattern: 3, 12, 48, 192,…