#### BOYER WRITESN.W.BOYER…Christian Author ## The Finger Print of God

Leonardo Pisano, born  1170 in Pisa near the famous leaning tower,  is better known as  Fibonacci.

Fibonacci   was educated in North Africa where his father, Guilielmo, held a diplomatic post. His father’s job was to represent the merchants of the Republic of Pisa who were trading in Bugia, later called Bougie and now called Bejaia. Bejaia is a Mediterranean port in northeastern Algeria.

So, you do not remember him?    Perhaps not, if math is not your forte, but he has influenced your life greatly since you began adding 2+2. The way we add and subtract today from elementary school to the accountant to whom you may be making a visit soon….use methods of math that were not previously used.  He wrote, by hand, a number of books explaining his mathematical ideas.

Called the  Fibonacci series, the sequence in which each number is the sum of the two preceding numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, …  (each number is the sum of the previous two).

His  is a simple series, but its ramifications and applications are nearly limitless. It has fascinated and perplexed mathematicians for over 700 years

One of his books was Liber quadratorum, written in 1225.  .The book’s name means the book of squares. It also examines methods to find Pythogorean triples. Fibonacci first notes that square numbers can be constructed as sums of odd numbers, essentially describing an inductive construction using the formula n2 + (2n+1) = (n+1)2.

Fibonacci writes:-

I thought about the origin of all square numbers and discovered that they arose from the regular ascent of odd numbers. For unity is a square and from it is produced the first square, namely 1; adding 3 to this makes the second square, namely 4, whose root is 2; if to this sum is added a third odd number, namely 5, the third square will be produced, namely 9, whose root is 3; and so the sequence and series of square numbers always rise through the regular addition of odd numbers.

To construct the Pythogorean triples, Fibonacci proceeds as follows:-

Thus when I wish to find two square numbers whose addition produces a square number, I take any odd square number as one of the two square numbers and I find the other square number by the addition of all the odd numbers from unity up to but excluding the odd square number. For example, I take 9 as one of the two squares mentioned; the remaining square will be obtained by the addition of all the odd numbers below 9, namely 1, 3, 5, 7, whose sum is 16, a square number, which when added to 9 gives 25, a square number”

_________________To all who may be ready to throw in the towel, perhaps we should see a video that helps explain all this for those of us who had math teachers who sat on the desk and talked basketball.