Fibonacci also known as Leonardo de Pisa knew very little about the power of the sequences he had found after discovering the Hindu-Arabic numerals and figures in the year 1200. Little did he know that the Fibonacci sequence he found from the counting of Rabbits was the answer to all of life’s questions and that he had found the part of the codes of the secret of how the universe proliferates. His famous sequences which permeates all of nature in the form of the Golden Ratio would be the platform on which all of life can be explained in the universe. His discovery was rooted in the Hindu system of numbers known as the Vedic Codes of Life part of the ancient Vedic Mathematics of the Hindus refer to sometimes as the “Vedanta Sciences” . Here in this wonderful manual, Swami Ram will illustrate the the relationship of the Fibonacci Sequences , the Golden Ratio and the Cycles of the Universe to the Vedic Codes which incorporates the Nine Hindu Numerals as well as the Zero to explain why all that we experience in nature happens when it it does. This includes Natural disasters, the spiral growth of all human experiences as well as all cycles that each one of us goes through every minute, every day , every month and every year. The enigma of this combination of the Vedic Codes with the Fibonacci sequences is of such a nature that one cannot imagine the amazing discoveries that lies ahead and consequential effects it will have on our concept of life, the financial markets as well as the future of our world. It truly is an age changing science appropriately prepared for the 2012 world consciousness

 

A LITTLE HISTORY OF LEONARDO DE PISA ALSO KNOWN AS MR. FIBONACCI

The following are texts taken from the book “THE MAN OF NUMBERS” by Keith Devlin. If you need to read more on this I recommend purchasing that book.

The Arabs viewed mathematics in a very practical manner, as something to be used by traders, land surveyors, and engineers, and wrote texts for those professional people, so Fibonacci’s father  could well have seen the Hindu-Arabic system as a powerful new tool that would benefit his son.

Much of what we know about Leonardo Fibonacci’s time in Bugia comes from the brief prologue with which be began his first book, Liber abbaci. The first part describes the approach his book takes.

You, my Master Michael Scott, most great philosopher, wrote to my Lord about the book on numbers which some time ago I composed and transcribed to you; whence complying with your criticism, your more subtle examining circumspection, to the honor of you and many others I with advantage corrected this work. In this rectification I added certain necessities, and I deleted certain superfluities. In it presented a full instruction on numbers close to the method of the Indians, whose outstanding method I chose for this science. And because arithmetic science and geometric science are connected, and support one another, the full knowledge of numbers cannot be presented without encountering some geometry, or without seeing that operating in this way on numbers is close to geometry; the methods is full of many proofs and demonstrations which are made with geometric figures. And truly in another book that I composed on the practice of geometry I explained this and many other things pertinent to geometry, each subject to appropriate proof. To be sure, this book looks more to theory than to practice. Hence, whoever would wish to know well the practice of this science ought eagerly to busy himself with continuous use and enduring exercise in practice, for science by practice turns into habit; memory and even perception correlate with the hands and figures, which as an impulse and breath in one and the same instant, almost the same, go naturally together for all; and thus will be made a student of habit; following by degrees he will be able easily to attain this to perfection. And to reveal more easily discover. Further, if in this work is found insufficiency or defect, I submit it to your correction.

At this point, the prologue changes direction, as Leonardo recounted how he came to learn this remarkable new calculating method, thereby providing the only autobiographical information we have about its author. Why he included this is unknown. Like mathematicians before and after him, Leonardo cared little for the history of the discipline. Mathematics is eternal, and exactly when something new is discovered and by whom is of secondary importance. Mathematicians admire those who make great discoveries, but their interest is generally in what is discovered, not in who got there first. Nevertheless, described was a monumental one, and at the back of his mind may have lurked the notion that one day people would wonder how this great Hindu invention found its way from the Muslim scholars and merchants who had held it for many centuries to the practical trading men of northern Europe. In any event, he broke with tradition and inserted an all-too-brief summary of the part he played in the story.

As my father was a public official away from our homeland in the Bugia customs house established for the Pisan merchants who frequently gathered there, he had me in my  youth brought to him, looking to find for me a useful and comfortable future; there he wanted me in the study of mathematics and to be taught for some days. There from a marvelous instruction in the art of the nine Indian figures, the introduction and knowledge of the art pleased me so much above all else, and I learned from them, whoever was learned in it, from nearby Egypt, Syria, Greece, Sicily, and Provence, and their various methods, to which locations of business I traveled considerable afterwards for much study, and I learned considerably assembled disputations. But this, on the whole, the algorithm and even the Pythagorean arcs, I still reckoned almost an error compared to the Indian method.* Therefore strictly embracing the Indian method, and attentive to the study of it, from mine own sense adding some, and some more still from the subtle geometric art, applying the sum that I was able to perceive to this book, o worked to put it together in xv distinct chapters, showing certain proof for almost everything that I put in, so that further, this method perfected above the rest, this science is in strutted to the eager, and to the Italian people above all others, who up to now are found without a minimum. If, by chance, something less or more proper or necessary I omitted, your indulgence for me is entreated, as there is no one who is without fault and in all things is altogether circumspect.

*recall that Gerbert (ca.980) used the Hindu-Arabic numerals on counters as part of a primitive form of abacus, on which triples of columns were marked with an arc. These were called Pythagorean arcs. When he wrote numbers, Leonardo followed the system of triples, just as we do today when we write numbers like 1,395,281. Leonardo told his readers that even with various enhancements, abacus methods were no match for Hindu-Arabic arithmetic.

The book begins with an observation about numbers that seems trivial to modern readers but was profound during the time of the great Arabic mathematician Al-Khwarizmi:

When I consider what people generally want in calculating, I found that it always is a number. I also observed that every number is composed of units, and that any number may be divided into units. Moreover, I found that every number which may be expressed from one to ten, surpasses the preceding by one unit: afterwards the ten is doubled or tripled just as before the units were: thus arise twenty, thirty, etc. until a hundred: then the hundred is doubled and tripled in the same manner as the units and the tens, up to a thousand; …so forth to the utmost limit of numeration.

Understanding what al-Khw?rizm?, meant requires an appreciation that in his day numbers were regarded as different from quantities of length, a distinction still made in the seventeenth century when Newton invented calculus. The great Arabic mathematician was actually making an uncannily accurate prediction about the degree to which numbers would come to dominate mathematics.

Leonardo divided the book into fifteen chapters, the titles of which vary from manuscript to manuscript, suggesting that the scribes who made copies felt free to make what they felt were clarifying improvements. The titles in Sigler’s English translation are:

Dedication and prologue

1                     on the recognition of the nine Indian figures and how all numbers are written with them; and how the numbers must be held in the hands, and on the introduction to calculations..

2                     and so on

His opening chapter describes how to write and read whole numbers in the Hindus’ decimal system. Leonardo began: “These are the nine figures of the Indians: 9 8 7 6 5 4 3 2 1. With these nine figures, and with this sign 0 which in Arabic is called zephirum, any number can be written, as will be demonstrated.” He went on to explain the principles of place value, describing the forms of the numerals, and showing how to write large numbers (either by putting a dot –adcentare-above each hundred, and below each thousand, or by linking group of there numerals with a small curved stoke called a virgule). When his chapter title promised to explain “how the numbers must be held in the hands,” he meant that quite literally. He described a procedure to calculate on the fingers, widely used by medieval scholars and traders, which was regarded as the easiest and quickest way of performing calculations. Manuscript copies of Liber abbaci and those of many other arithmetic books that were to follow often included a drawing showing the various finger positions used to represent different whole numbers. Leonardo also provided addition and multiplication tables to be referred to or memorized in order to facilitate computations. In all, he devoted several pages to this introductory description of the numerals, which would have been his readers’ first encounter with modern numbers.

 

LEONARDO FIBONACCI DISCOVERS THE ZERO – STARTS THE ARITHMETIC REVOLUTION

The following are texts taken from the book “THE MAN OF NUMBERS” by Keith Devlin. If you need to read more on this I recommend purchasing that book.

Paralleling the growth of the abacus books was the growth throughout Italy of arithmetic schools, called scuole d’abbaco or botteghe d’abbaco (abacus schools), where young children were taught how to use the Hindu-Arabic number system. The earliest record of an abacus school is in the statutes of the commune of Verona in 1294, which mention the appointment of maestro Lotto of Florence to teach mathematics. The teachers in such schools were known as maestri d’abbaco (teachers of abacus, or more colloquially, arithmetic teachers). In addition to teaching children in the schools, many of them taught other adults, who learn to use the system in the commercial world or would themselves become organizers of, and teachers in, the schools.

The maestri d’abbaco followed a specified syllabus, typically composed of reading and writing in the vernacular, arithmetic, geometry, bookkeeping, and occasionally navigation. The most detailed syllabus know today is from the school of Cristofano di Gherardo di Dino, who taught in Pisa in 1442.

This is the way of teaching the abacus in Pisa, from the beginning to the end of the students’ learning period, as we will say.

1. At first, when the boy begins schools he is taught how to make figures, that 9, 8 , 7, 6, 5, 4, 3, 2, 1;
2. Then he is taught how to keep numbers in his hands, that is his left hand units and tens and in his right hand hundreds and thousands;
3. Then to draw numbers on tables: that is of two figures what it means, and then three figures, four figures and so on. Then how to keep them in one’s hand.
4. Then one explains the tables of multiplication. One draws it on the table, starting form one times one until ten times ten one hundred, and students learn it very well by heart.
5. Then one teaches how to make divisions;
6. Then how to multiply fractions;
7. Then how to sum fractions;
8. Then how to divide {fractions};
9. Then how to accrue simple interests and the “new year’s merit”;
10. Then how to measure lands or how to square a number;
11. Then how to make simple discounts and new year’s discounts;
12. then how to calculate the ounces of silver;
13. Then the melting of silver;
14. Then one makes the comparison between the two amounts;
15. And note that to make the above-mentioned calculations, students are to use pencils according to their level. And sometimes have them sum with their hands, or else on the blackboard; occasionally give them some extraordinary homework, according to the teacher’s will.
16. Please, note also this general rule: every evening give them homework for the following day according to their level. And, in case of days of rest, homework is to be doubled.

Once students at an abacus school l had learned the basics of the Hindu-Arabic number system and its arithmetic, they were shown how to solve practical problems, such as the everyday exchange of different types of goods or currencies. Other problems might deal with the distribution of profits, where each member invested a certain sum and may have later withdrawn a portion of that amount.

With Pisa in decline not long after Leonardo’s death, by the fifteenth century Florence had become a major locus for much of the activity in the new arithmetic and its application, particularly in the field of finance. Insight into the growth in use of the Hindu-Arabic numbers in finance comes from examining the ledgers of the Medici Bank. The Medici family, mentioned for the first time in a document of 1230, came from the agricultural Mugello region, north of Florence. Their rise to prominence began under Cosimo de’ Medici during the late fourteenth century. Having acquired their wealth in the textile trade, in 1937 they founded the Medici Bank, which became Europe’s largest and most respected bank during the fifteenth century, when it had at least eight trading houses throughout Europe. The Medicis’s lasting contribution to business, commerce, and accounting was the development of the double-entry bookkeeping system for tracking credits and debits. Although its origins can be traced back to Roman times, the system in its modern form was first used by accountants working for the Medici family in Florence. In the Medici account books from 1406 onward, Hindu-Arabic numbers began to appear frequently in the narrative or descriptive column. From 1439 onward they replaced Roman numerals in primary entries (journals, wastebooks, etc.), but no until 1482 were Roman numerals abandoned in the final business ledger of all but one Medici merchant. From 1494 onward, only Hindu-Arabic numerals were used in al Medici account books.