L'Italo-Americano

THURSDAY, NOVEMBER 28, 2024 www.italoamericano.org 14 L'Italo-Americano F ibonacci (fi - son - of Bonacci), born a s L e o n a r d o o f Pisa in 1175, was a mathematician whose contributions laid the g r o u n d w o r k f o r m o d e r n m a t h e m a t i c s a n d f o r e v e r changed the way numbers were understood and used in Europe. As the son of a mer- chant, he grew up in a world of commerce and travel: his father's work in Bugia (mod- e r n - d a y B é j a ï a , A l g e r i a ) e x p o s e d F i b o n a c c i t o t h e Hindu-Arabic numeral sys- t e m . T h i s s y s t e m , v a s t l y more efficient than Roman numerals, fascinated him and inspired the mathemati- cal works for which he is remembered today. I n 1 2 0 2 , F i b o n a c c i authored the Liber Abaci (The Book of Calculation), which introduced the Hindu- Arabic numeral system to the Western world. The book explained how these num- bers could simplify calcula- tions, making them practical for trade and everyday life. Among the many examples i n t h e L i b e r A b a c i , o n e stands out for its brilliance and relevance: the Fibonac- c i s e q u e n c e , a series of numbers starting with 0 and 1 , w i t h e a c h s u b s e q u e n t number being the sum of the two preceding ones — 0, 1, 1, 2, 3, 5, 8, 13, and so on. The Fibonacci sequence reveals a hidden order in nature, art, and even the human body, and it is inti- m a t e l y c o n n e c t e d t o t h e golden ratio, often called the "divine proportion" and denoted by the Greek letter phi (approximately 1.618). When dividing one Fibonac- ci number by the one before it, the result approaches phi as the sequence progresses. This number has fascinated mathematicians, artists, and philosophers for centuries because it is considered a symbol of beauty, harmony, and balance. In nature, the divine pro- portion can be observed in the spirals of galaxies, the whorls of hurricanes, the arrangement of sunflower seeds, and the shells of mol- l u s k s ; t r e e s g r o w t h e i r branches and leaves accord- ing to the sequence, ensur- ing optimal exposure to sun- light, and even honeybee colonies reflect Fibonacci's n u m b e r s : t h e r a t i o o f f e m a l e s t o m a l e s a l w a y s a p p r o x i m a t e s p h i . T h e sequence also governs the arrangement of petals on flowers, ensuring the most efficient use of space. These patterns, repeated across such diverse forms of life, suggest a universal prin- ciple of design. The golden ratio is also present in the proportions of the human body: for instance, the ratio of your height to the distance from your feet to your navel, or the length of your arm to your forearm, both approxi- mate phi. This mathematical harmony led some to believe that phi represents a divine blueprint, a belief shared by a n c i e n t s c h o l a r s w h o referred to it as the "divine p r o p o r t i o n . " A r t i s t s a n d architects throughout history incorporated it into their m a s t e r p i e c e s t o e v o k e a s e n s e o f n a t u r a l b a l a n c e . Leonardo da Vinci, for example, utilized the golden ratio in his famous drawing o f t h e V i t r u v i a n M a n , which demonstrates the ideal h u m a n p r o p o r t i o n s d e s c r i b e d b y t h e R o m a n architect Vitruvius. Similar- ly, the golden ratio is embed- ded in the structure of the Great Pyramid of Giza, the Parthenon in Athens, and the façade of Santa Maria N o v e l l a i n F l o r e n c e , designed by Leon Battista Alberti. Even modern icons like Apple's logo and credit card dimensions reflect this timeless proportion. But Fibonacci's contribu- tions extended beyond the s e q u e n c e f o r w h i c h h e i s most famous: in the Liber Abaci, he also introduced algebraic concepts, quadratic and cubic equations, and the c o n c e p t o f z e r o , w h i c h revolutionized mathematics in Europe. Before Fibonacci, the Western world relied on c u m b e r s o m e R o m a n numerals, which lacked the simplicity and functionality of the Hindu-Arabic system. By bringing these ideas to Italy, Fibonacci enabled the flourishing of science, com- Advancing our Legacy: Italian Community Services CASA FUGAZI If you know of any senior of Italian descent in San Francisco needing assistance, please contact: ItalianCS.org | (415) 362-6423 | info@italiancs.com Italian Community Services continues to assist Bay Area Italian-American seniors and their families navigate and manage the resources needed to live healthy, independent and productive lives. Since Shelter-in-Place began in San Francisco, Italian Community Services has delivered over 240 meals, over 900 care packages and made over 2000 phone wellness checks for our seniors. merce, and art during the Renaissance. The origins of Fibonacci's s e q u e n c e , h o w e v e r , w e r e surprisingly humble. During a mathematical competition in Pisa, attended by Holy Roman Emperor Frederick II, Fibonacci solved a prob- lem involving the reproduc- tion of rabbits. The question w a s d e c e p t i v e l y s i m p l e : starting with one pair of rab- bits, how many pairs would exist after a year if every pair produced a new pair each month, beginning in their s e c o n d m o n t h o f l i f e ? Fibonacci's solution pro- d u c e d t h e s e q u e n c e t h a t bears his name. The Italian mathemati- cian's legacy continues to inspire scientists, artists, and thinkers. And there is even a day dedicated to him, November 23, because the date—11/23—represents the s t a r t o f t h e F i b o n a c c i sequence (1, 1, 2, 3). Fibonacci's story reminds us that mathematics are not an abstract discipline in the end, but a way to understand the world's underlying pat- terns in a universe ultimate- ly governed by beauty and order. Far from being a relic of the past, Fibonacci's dis- coveries continue to shape our understanding of the world, demonstrating that mathematics, at its core, is a bridge between the physical and the metaphysical, the mundane and the divine. Fibonacci and the numbers that shape the Universe FRANCESCA BEZZONE LIFE PEOPLE PLACES HERITAGE TRADITIONS A Fibonacci spiral showing the Golden Ratio (Photo: Altitudevs/Dreamstime)

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