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Inetrobe is an enclave of new-age e-movers. We use catchy names for our job titles, like Vision Guidance Leader instead of Consultant. Cool names make us sound smarter and more clever. |
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The human mind is a chatterbox that is always looking for reason and order. We want to bring order to chaos because we have survived and evolved precisely because of our ability to look for and find abstract metaphysical patterns in the natural world. We can see it in our language, culture, music, religion…
Mystery novels and movies are popular because they show us how something seemingly random can in fact be described by a very logical pattern that is revealed by a clever detective. In the example on this page we can see how the Fibonacci sequence can be used to describe many natural occurrences. We can even see that same pattern in the human form. We can see how with the use of the Bezier curve we can find a correlation with the Fibonacci sequence and the symmetry of the human form as described by Leonardo da Vinci. This need for humans to find patters in chaos can be exploited sometimes inadvertently by politicians and leaders. President Kennedy is assassinated by a seemingly random and pointless act of violence and yet we look for conspiracy theories to explain a complex rationality behind this random act. A terrorist act occurs and our immediate reaction is to ask why? We want to find a pattern or reason for this act again some of us would like to turn to conspiracy theories but still others hear our politicians tell us a simple but compelling narrative about how we must return this violence in kind. We can see how with the use of the Bezier curve we can find a correlation with the Fibonacci sequence and the symmetry of the human form as described by Leonardo da Vinci. |
This need for humans to find patters in chaos can be exploited sometimes inadvertently by politicians and leaders. President Kennedy is assassinated by a seemingly random and pointless act of violence and yet we look for conspiracy theories to explain a complex rationality behind this random act. A terrorist act occurs and our immediate reaction is to ask why? We want to find a pattern or reason for this act again some of us would like to turn to conspiracy theories but still others hear our politicians tell us a simple but compelling narrative about how we must return this violence in kind. Religion used by those who seek to legitimate their authority by telling us that they can explain and control the randomness of life through logic games. They tell us that our destiny is controlled my spiritual forces that can alleviate our suffering. We are told that our relationships with these forces are based on mutual reciprocity and we must obey religious leaders in order to know and understand the random forces that control our lives. This can partially explain our propensity to organized rituals. The kind of person who would say there is no such thing as a witch would be the first to be considered a witch. Authority is the source of belief. We find beauty in abstract patterns because it has helped our survival but we have survived because we find abstract patterns beautiful. But if we cannot look critically at our belief systems we risk becoming slaves to our fear. Descartes said “I think and therefore I am” or more accurately translated “I question and therefore I am”. If we take this one step further this statement might be interperated as “I have the ability to question and therefore I am” or “I have the ability to question my own existence and therefore I am” It is this ability for humans to think of ourselves in the abstract context of existence that makes us unique. Our language is filled with metaphysical ideas that have no physical form such as love, hate, kindness… These concepts are as real as the air we breath yet they only exist in our minds. However, it is Buddhist philosophy that that tells us that all physical things in this world “Sum Sara” are based on impermanence and it is only reality are those things which are not based on the physical world. Again we find our minds seeking to find explanation and rational patterns to these mysteries. |
Leonardo of Pisa (1170s or 1180s – 1250), also known as Leonardo Pisano, Leonardo Bonacci, Leonardo Fibonacci, or, most commonly, simply Fibonacci, was an Italian mathematician, considered by some "the most talented mathematician of the Middle Ages"[1].
Fibonacci is best known to the modern world for:[2]
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Leonardo was born in Pisa. His father Guglielmo was nicknamed Bonaccio ("good natured" or "simple"). Leonardo's mother, Alessandra, died when he was nine years old. Leonardo was posthumously given the nickname Fibonacci (derived from filius Bonacci, meaning son of Bonaccio).[4]
Guglielmo directed a trading post (by some accounts he was the consultant for Pisa) in Bugia, a port east of Algiers in the Almohad dynasty's sultanate in barbaresque North Africa (now Bejaia, Algeria). As a young boy, Leonardo traveled there to help him. This is where he learned about the Hindu-Arabic numeral system.
Recognizing that arithmetic with Hindu numerals is simpler and more efficient than with Roman numerals, Fibonacci traveled throughout the Mediterranean world to study under the leading Arab mathematicians of the time. Leonardo returned from his travels around 1200. In 1202, at age 32, he published what he had learned in Liber Abaci (Book of Abacus or Book of Calculation), and thereby introduced Hindu-Arabic numerals to Europe.
Leonardo became an amicable guest of the Emperor Frederick II, who enjoyed mathematics and science. In 1240 the Republic of Pisa honoured Leonardo, referred to as Leonardo Bigollo,[5] by granting him a salary.
In his Liber Abaci, Fibonacci introduces the so-called Modus Indorum (method of the Indians), today known as Arabic numerals, as follows (Sigler 2003; Grimm 1973):
After my father's appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and in view of its future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days.
There, following my introduction, as a consequence of marvelous instruction in the art, to the nine digits of the Hindus, the knowledge of the art very much appealed to me before all others, and for it I realized that all its aspects were studied in Egypt, Syria, Greece, Sicily, and Provence, with their varying methods; and at these places thereafter, while on business.
I pursued my study in depth and learned the give-and-take of disputation. But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in respect to the method of the Hindus. (Modus Indorum). Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid's geometric art, I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters.
Almost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it, as they have been up to now. If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things.
The nine Indian figures are:
9 8 7 6 5 4 3 2 1
With these nine figures, and with the sign 0 ... any number may be written.
Thus, Liber Abaci advocated numeration with the digits 0–9 and place value. The book showed the practical importance of the new numeral system, using lattice multiplication and Egyptian fractions, by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. The book was well received throughout educated Europe and had a profound impact on European thought. Nevertheless, the use of decimal numerals did not become widespread until the invention of printing almost three centuries later, in 1585 (see, e.g., Ptolemy's world map printed in 1482 by Lienhart Holle in Ulm).
Liber Abaci also posed, and solved, a problem involving the growth of a hypothetical population of rabbits based on idealized assumptions. The solution, generation by generation, was a sequence of numbers later known as Fibonacci numbers. The number sequence was known to Indian mathematicians as early as the 6th century, but it was Fibonacci's Liber Abaci that introduced it to the West.
