Sunday, October 05, 2014

The Curious Marriage of Fibonacci Numbers and Surnames



Fibonacci Number is a number from the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ..... This sequence is a very remarkable sequence of numbers which has far and wide consequences. An Italian mathematician Leonardo Pisano alias Fibonacci is credited to have studied about this sequence and documented for the first time, after observing rabbit breeding properties.
What has Fibonacci Number to do with surnames? This observation was instigated by a recent reading of the male honeybees and their ancestry. A female honeybee is born from a fertilized egg whereas a male honeybee is from an unfertilized egg. Hence a male honey bee has only one parent. If we trace the ancestry of a male honeybee, we get the number of ancestors in each level as 1, 2, 3, 5, 8, ... . This is nothing but a Fibonacci Sequence.
Let us come to the case of surnames. Conventionally a child can inherit the surname of its father or mother.  A girl after her marriage can take the surname of her husband. However, a boy seldom takes the surname of his wife after marriage. This observation helps us to count the number of possible surnames of a boy and a girl.

A married woman can either retain her surname or accept that of her husband. Hence, a married woman has three possible surnames. This is pictorially represented below:


At any level, we could see that the number of possible surnames at any level is a Fibonacci Number. It is not just that! Spot anyone, man or woman, in this diagram and count from there: we still get a Fibonacci Sequence as a subsequence. Isn't it curious?