Page 47 - Ramanujan Yatra

Ramanujan
YATRA
38
5
29
1.6111111
6
47
1.6206897
7
76
1.6170213
8
123
1.6184211
9
199
1.6178862
10
322
1.6180905
11
521
1.6180124
12
843
1.6180422
13
1364
1.6180308
14
2207
1.6180352
15
3571
1.6180335
16
5778
1.6180342
17
9349
1.6180339
18
15127
1.618034
19
24476
1.618034
20
39603
1.618034
21
64079
1.618034
Figure 4: The ratio of successive terms remains invariant even if the initial values of the sequence are changed.
Graphing Column C further revealed the steadying behaviour of the Fibonacci like sequence as shown in Figure 5. This was indeed an interesting observation for students and many wanted to know the reason behind this ‘magic’!
1.8 1.7
1.6 1.5
1.4
1 4 7
10 13
16 19 2 2 2 5 2 8 3 1 3 4 3 7 4 0 4 3 4 6 4 9
Figure 5: The ratios settle down to 1.618 (up to 3 decimal places) Following mathematical explanation was then provided to the students.