Mysteries and Secrets of Numerology. Patricia Fanthorpe

Чтение книги онлайн.

СКАЧАТЬ language, “11” is hamaika; “7” is hazpi, and “3” is hiru. Their interest in “11” as having special numerological significance relates to “11” being the first number that cannot be counted with the hands alone. In the sequence of prime numbers, it is the fifth: 2, 3, 5, 7, 11. There are some very strange calculations connected with the number “11.” For example, to check whether a number is exactly divisible by 11, add every alternate digit, then add the remaining digits and subtract one total from the other. If the answer is “0,” or a multiple of 11, the large number will divide by 11. For example, consider 2,592,821. Consider the equation 2+9+8+1=20 followed by 5+2+2=9. Subtract 9 from 20, resulting in 11. This reveals that the large number 2,592,821 is divisible by 11. When the division is done, the answer is 2,592,821÷11=235,711 — an answer that consists of the first 5 prime numbers.

      A polygon with 11 sides is called an “undecagon” or a “hendecagon,” and has special significance for numerologists. A regular hendecagon can have a spindle placed through its centre, so that it can be used as a spinner — the equivalent of a miniature roulette wheel. The numbers 1–9 are marked on 9 of its sides, and two extra “1”s fill the last 2 sides to represent “11.” When the undecagon settles on any of the “1”s it is considered to be very positive and to bring good fortune to the person who spun it. If this occurs on 3 consecutive occasions, it is thought to bring either great fortune or deep and lasting romantic fulfilment.

      There are points throughout the history of numerology at which numerology blends into general magic involving spells and charms: so many movements of the hands, so many repetitions of an incantation, so many portions of each ingredient, the dates and times at which the spell can be enacted with the greatest likelihood of success. The same is true of the interaction between alchemy and numerology: for the alchemical processes to work, the alchemist believed that a particular blend of ingredients had to be assembled, and that the numbers of each, and the temperatures reached, were all significant for the work.

      The history of numerology, with its global ramifications and its intertwining with scientific mathematics, is a difficult path to follow, but it can be summed up as the route that perceptive and thoughtful numerologists have followed in order to reach the interesting forms of numerology that are practised today.

      4

       The Mysterious Fibonacci Numbers

       and the Golden Mean

      Two of the most intriguing sets of numbers that are of interest to scientific mathematicians as well as numerologists are the Fibonacci numbers and the golden mean, which are closely bonded to one another.

      The brilliant Italian mathematician and numerologist generally known as Fibonacci was born in 1170 and died at the age of 80 in 1250. His full name was Leonardo Pisano Bigollo, and he was referred to by a few different names, including Leonardo of Pisa, Leonardo Fibonacci, and Leonardo Bonacci. Historians of numerology and mathematics regard him as the outstanding genius of the Middle Ages in those allied fields.

      Fibonacci’s father, Guglielmo Fibonacci, was a very prosperous Italian merchant who was in charge of a busy trading post in Bugia, which was then a port belonging to the Almohad Sultanate in what is now Algeria. Bugia is currently known as Bejaia. As a youngster, Fibonacci travelled with his father to assist him with the demanding work of the trading post, and in the process, the young and gifted mathematician learned all about the numerals used by Hindus and Arabians. He saw almost immediately that these were much easier to manipulate than the Roman numerals that he had grown up with in Italy.

      Captivated by the relative ease and simplicity of using the Hindu-Arabic numerals, young Fibonacci went in search of the top mathematicians and numerologists in the whole of the Mediterranean area. In his early 30s he came back from these extensive study-travels and set down his findings in an exceptionally important mathematics textbook called Liber Abaci, which translates as “The Book of Calculations.” It was largely due to the circulation of Fibonacci’s treatise that the Hindu-Arabic numerals spread all over Europe. This was close to the start of the thirteenth century.

      Scholars and academics such as Fibonacci depended on the sponsorship of friendly and enlightened rulers like the Emperor Frederick II, who was himself interested in numerology, mathematics, and science. Frederick and Fibonacci became friends and Fibonacci lived as Frederick’s guest for some time. When he was 70, Fibonacci was honoured with a salary given to him by the Republic of Pisa and a statue to him was erected during the nineteenth century: a fitting tribute to an outstanding mathematician and numerologist.

      Indian mathematicians had already devised the mysterious series of numbers that bears Fibonacci’s name as early as the sixth century, but it was his popularizing of it in the twelfth century that made it widely known to numerologists and mathematicians in Europe. In his book, Liber Abaci, Fibonacci created and then solved a mathematical problem involving an imaginary population of rabbits. What Fibonacci came up with was a series of numbers for succeeding generations of his imaginary rabbits, which was created by starting with 0, followed by 1. Each subsequent number is found by adding its 2 predecessors together. This gives the start of the Fibonacci numbers as: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181 … and so on.

      There is an equally important and closely allied series, which is referred to as the Lucas Numbers. These were the work of Edouard Lucas (1842–1891), a brilliant French mathematician, who is probably best remembered for inventing his Tower of Hanoi puzzle, consisting of 3 columns and discs of varying sizes that have to be moved from 1 column to another while observing the rules of the game, which are that only 1 disc may be moved at a time and no disc may ever be placed on top of a smaller disc. He observed the Fibonacci principle of adding 2 preceding numbers to obtain the next number in the sequence. However, where Fibonacci started with 0, 1, 1, 2, 3, 5, and so on, Lucas began with “2” followed by “1,” then “3,” then “4,” “7,” “11,” “18,” and so on. When 2 consecutive Lucas numbers are divided they will also give ф, or its reciprocal. Just as with the Fibonacci series, the higher up in the series the numbers are, the more closely will their divisions approximate to the ф ratio and its reciprocal. The Greek letter ф (phi) is the twenty-first letter of the Greek alphabet, and is used in the same way as π (pi), the sixteenth letter, to express an irrational number such as 1.6180339 ... or 3.1416....

      The Fibonacci series has a very close link with the equally mysterious ratio represented by the Greek letter phi. This ratio can be written as 1.61803398874.… Geometrically, it refers to 3 lines, which are divided so that the ratio of the full line to the longer of its 2 sections is the same as the ratio of the longer section to the shorter section.

      ____________________________________________Whole line A

      _____________________________Longer section B

      Shorter section C _____________

      The ratio of A to B is the same as the ratio of B to C.

      That ratio is ф which is 1.61803398874 …

      This ratio has been used for centuries in art, architecture, and design work. It has even been found in some musical compositions.

      Phi (ф) can be found by dividing 2 adjacent Fibonacci numbers. The higher up the Fibonacci series we go, the closer the result is to ф.

      8÷5=1.6

      13÷8=1.625

      21÷13=1.61538

      34÷21=1.619

      4181÷2584=1.618034

      This can also be expressed algebraically: a+b divided by a=a, divided СКАЧАТЬ