# Section3Medieval 8ΒΆ permalink

Shortly after Pythagoras enjoyed his daily swims, mathematicians in India developed the place value number system that we use today, a system in which the quality of \(8\) shines. Although the ancient Greeks unearthed true gems of mathematical beauty, they represented numbers geometrically. The place value number system of India represented an important shift in the way we think about and manipulate numbers. This system found its way to Europe in medieval times, thanks to Islamic mathematicians. In 1202 A.D., in what is present day Italy, a young man named Leonardo of Pisa published *Liber Abaci*, a textbook on arithmetic. Chapter 1 opens with this sentence (see [6],p.102):

These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with the sign 0 which in Arabic is called

zephirum, any number can be written, as will below be demonstrated.

The author, better known to the world today as Fibonacci, went on to demonstrate basic arithmetical operations using these numerals and to include exercises involving rabbits, as all good texts must. The most famous problem in the book asks:

How many pairs of rabbits will be produced each month, beginning with a single pair, if every month each productive pair bears a new pair which becomes productive from the second month on?

This question yielded the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34,... . Yes, \(8\) is a Fibonacci number, a feather in any number's cap. What separates \(8\) from the others is its *position* in the list. It is the 6th term, and 8-6 is 2, and 2 is a prime factor of 8. No other Fibonacci number has this distinction. That is, if we let \(F_n\) denote the \(n\)th Fibonacci number and define the set

then \(A = \{8\}.\)

\(8\)'s title as the most interesting Fibonacci number was reinforced by the discovery in 1888 of the Chiquimula Chocolate Bar Scroll, which scholars believe was written in the 13th century. Translated, it reads:

Let a bar of chocolate be found simultaneously by five strangers, and let the bar consist of 10 squares, in the natural way, arranged in two rows of five. The strangers agree that each ought to receive 2 squares, and that their 2 squares be of one piece, whole, and unbroken. In how many ways might they distribute the treasure so as to avoid bloodshed?

Today we recognize that this question is equivalent to finding the number of tilings of a \(2 \times 5\) grid by dominoes, and that the answer is \(8\) because, in general, the \(2 \times n\) grid has \(F_{n+1}\) tilings by dominoes.