Page 52 - Ramanujan Yatra
P. 52
Monkey’s Tail-Continued Fractions and Ramanujan
VSS Sastry
The story goes like this: Mahalanobis, the great statistician (who founded Indian Statistical Institute, Calcutta), was a student at oxford. On coming to know that Ramanujan was at oxford, he went in search of him. Ramanujan was cooking something in his room. To pick up a conversation Mahalanobis started “I found a good problem in Strand Magazine. In a residential street, two British officers have their houses. A common friend of these officers comes to see them. He starts from one end of the street and searches for houses number; while doing so he goes on adding one house number to the next till he reaches the first officer’s house. He enters it, after finishing his job, he start moving in the same street to the second officer’s house. He repeats his old habit of adding house members as he walks along. He finds the house and to his amazement finds that the first sum and second sum are the same. Then the magazine asks find the house numbers of officers.”
Ramanujan: “Did you get those numbers?”
Mahalanobis: Yes I did. After some calculation I found 1+2+3+4+5=15. First officer’s house is 6. Second officer’s house is at 9. Because 7+8=15.”
Ramanujan: Not only these two. It is a continued fraction. Mahalanobis: “What? A continued fraction?”
Ramanujan: ‘Yes. Take it down.
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Ramanujan
YATRA
