Leonardo Fibonacci Quotes

If by chance I have omitted anything more or less proper or necessary, I beg forgiveness, since there is no one who is without fault and circumspect in all matters.

Christianity initially rejected zero, but trade would soon demand it. The man who reintroduced zero to the West was Leonardo of Pisa. The son of an Italian trader, he traveled to northern Africa. There the young man-better known as Fibonacci-learned Mathematics from the Muslims and soon became a good mathematician in his own right.

When he was about fourteen years of age, Leonardo would have left the fondaco and most likely traveled with an older merchant, a form of apprenticeship system common in those days. Around that time his father summoned him to Bugia. No one knows exactly when he made this voyage. In the introduction to Liber abbaci, he later wrote: “When my father, who had been appointed by his country as public notary in the customs at Bugia acting for the Pisan merchants going there, was in charge, he summoned me to him while I was still a child, and having an eye to usefulness and future convenience, desired me to stay there and receive instruction in the school of accounting.

There was no escaping math, after all. It was everywhere, especially in nature. You could go as far to say that math was nature. Pi describe the arc of a rainbow, the way ripples spread in a body of water, the dimensions of the moon and sun. Fractals could be observed in halved sections of red cabbage, the topography of deserts, the branching of lightning bolts. And take the old man glaring out from his shirt, Leonardo Fibonacci, who discovered that a basic number sequence predicted the arrangement of scales on a pinecone, the distribution of petals on flowers, the spiral of a snail shell, the furcation of veins in the human body, even the structure of DNA. When all the people were gone, the numbers would persist.

Having described the basic methods of Hindu-Arabic arithmetic in the first seven chapters, Leonardo devoted most of the remainder of the book to practical problems. Chapters 8 and 9 provide dozens of worked examples on buying, selling, and pricing merchandise, using what we would today call reasoning by proportions—the math we use to check the best deal in the supermarket.

Thus, the spirit of objective inquiry in understanding physical realities was very much there in the works of Muslim scientists. The seminal work on Algebra comes from Al-Khwarizmī and Fibonacci (Leonardo of Pisa) has quoted him. Al-Khwarizmī, the pioneer of Algebra, wrote that given an equation, collecting the unknowns on one side of the equation is called 'al-Jabr'. The word Algebra comes from that. He developed sine, cosine and trigonometric tables, which were later translated in the West. He developed algorithms, which are the building blocks of modern computers. In mathematics, several Muslim scientists like Al-Battani, Al-Beruni and Abul-Wafa contributed to trigonometry. Furthermore, Omar Khayyam worked on Binomial Theorem. He found geometric solutions to all 13 forms of cubic equations.

Manetti claims he was surveying the antiquities of Rome, measuring their heights and proportions. He fails to record what method Filippo used, but he could have determined the height of columns or buildings with an upright rod. This method would have been familiar to him from Leonardo Fibonacci’s Practica geometriae (1220), a work that was studied in the schools of Florence. Or he could have employed a quadrant or, even more simply, a mirror, whose use for mensuration Fibonacci likewise describes.

Leonardo Pisano, aka Fibonacci: Fibonacci was a 13th-century Italian mathematician who invented the Fibonacci series, which goes like this: 1, 1, 2, 3, 5, 8, 13, 21, etc. Each of the numbers is the sum of the two preceding numbers. I look at the sequence again. I know I recognize it from somewhere. It takes me a couple of seconds, but then it clicks: Boggle! It's the scoring system for my favorite find-a-word game, Boggle.