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Ever since ancient times, math and numbers were not only seen as a logical an rational process trought which reality could be descrived as postuleted.

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Presentation on theme: "Ever since ancient times, math and numbers were not only seen as a logical an rational process trought which reality could be descrived as postuleted."— Presentation transcript:

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2 Ever since ancient times, math and numbers were not only seen as a logical an rational process trought which reality could be descrived as postuleted by philosopher as Galileo Galilei, but as a mystery, a god’s gift, something arcane, or simply as something unreachable by human minds. That’s why only few people ventured in the world of maths, given her difficulty and a language not yet standardized as today, that made hard for scholars from different culture to understand each other’s discoveries. And that’s also the reason why the few that practiced it where priests, mages, philosopher, alchimists, sorcerers, or sages. This was especially true in the B.C. period, but even today math preserve her ancient mysterious nature and raises many legends around it. Let's discover some of them.

3 Golden ratio The golden ratio has fascinated Western intellectuals of diverse interests for at least 2,400 years. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics, since her presence ha been identified as an universal law present in nature. Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The Greeks usually attributed discovery of this concept to Pythagoras or his followers. Euclid's Elements (Greek: Στοιχε ῖ α) provides the first known written definition of what is now called the golden ratio: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less." Throughout theElements, several propositions and their proofs employ the golden ratio. Some of these propositions show that the golden ratio is an irrational number.

4 Fibonacci John Waskom postulated that stages of human development followed the Fibonacci sequence, indicating that the unfolding psychology of human life would ideally be a "living proof" of the Golden Mean. The Fibonacci numbers are a sequence of integers, starting with 0, 1 and continuing 1, 2, 3, 5, 8, 13,..., each new number being the sum of the previous two. The Fibonacci numbers, and in conjunction the golden ratio, are a popular theme in culture, as his pattern is directly linked to many natural entities as the pattern of the “sunflower”, which gives it its supernatural reputation. The Fibonacci sequence appears first in Indian mathematics, in connection with Sanskrit prosody (Versification of Sanskrit poetry). In the West, the Fibonacci sequence first appears in the book Liber Abaci (1202) by Leonardo of Pisa, known as Fibonacci

5 Pythagoreanism was the system of esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagorean cult, who were considerably influenced by mathematics. Pythagoreanism originated in the 5th century BC. They influenced almost everything that we know today, even if their studies were so mystical and secretive. Is said that Hippasus of Metapontum was a Pythagorean philosopher that discovered the existence of irrational numbers. The discovery is said to have been shocMaharaja the Pythagoreans, and Hippasus is supposed to have drowned at sea as a punishment from the gods for unraveling their secret. Pythagoreanism

6 Horus fractions The Eye of Horus was used as a notation of measurement, particularly for measuring the ingredients in medicines and pigments. The symbol was divided into six parts, representing the shattering of Horus´ eye into six pieces. Each piece was associated with one of the six senses and a specific fraction. More complex fractions were created by adding the symbols together. It is interesting to note that if the pieces are added together the total is 63/64 not 1. Some suggest that the remaining 1/64 represents the missing piece represented by the fact that perfection was not possible Others myths suggest that it is Horus' right eye which was torn out and that the myth refers to a solar eclipse in which the sun is momentarily blotted from the sky Horus was an ancient sky god whose eyes were said to be the sun and the moon. However, he soon became strongly associated with the sun while Thoth was associated with the moon. An ancient myth describes a battle between Horus and Set in which Horus´ right eye was torn out and Set lost his testicles. Thoth magically restored Horus´ eye, at which point it was given the name "Wadjet" ("whole" or "healthy"). In this myth it is specifically stated that it is Horus´ left eye which has been torn out, so the myth relates to the waxing and waning of the moon during which the moon appears to have been torn out of the sky before being restored once every lunar month.

7 Mayan calendar The fundamental mayan priestly sciences were arithmetics and calendrics. The priests had become customary to deify the numbers as well as the basic day-unit, and to conceive the mechanism of time as a sort of relay in which the 'burden' of the time-units was passed on from one divine numerical 'bearer' to the next one. The numbers were personified not by distinctive numerical deities, but by some of the principal general deities, who were thus seen to be responsible for the ongoing 'march of time'. The day-units were often depicted as the patrons of the priestly scribes and diviners themselves, that is, who seem to have been conceived as creator deities in their own right. In the Postclassic period, the time-unit of the was imagined as a divine Maharaja. Today, this uncanny precision and mass hysteria lend to think that the day the mayan calendar will end, closing its last circle, the world will know impressive changes, apocalypse, or some sort of revelation. The day is thought will be the 21/12/2012, but this date is often subject to change and misconceptions, so nobody knows if something eventually will happen or what will happen. The Maya calendar is a system of calendars which strongly relied on mysticism, astrology and magic, even if, as the pythagorean mathematic, it has been recognized a true masterpiece of cosmic observation thus not knowing how the mayans could have achieved such impressive precision in their work. By the Maya mythological tradition, the deity Itzamna is frequently credited with bringing the knowledge of the calendar system to the ancestral Maya, along with writing in general and other foundational aspects of Maya culture as math.

8 Kepler and music of spheres The Greek philosopher Pythagoras is frequently credited with originating the concept. At the time, the sun, moon, and planets were thought to revolve around Earth in their proper spheres. The spheres were thought to be related by the whole-number ratios of pure musical intervals, creating musical harmony. The following music is of course simply an attempt to recreate Kepler's mathematic formulas of the music of the spheres in real time. "I grant you that no sounds are given forth, but I affirm... that the movements of the planets are modulated according to harmonic proportions.". This music is a representation of those proportions. Johannes Kepler used the concept of the music of the spheres in his Harmonice Mundi Harmony of the Worlds in 1619. Kepler was convinced "that the geometrical things have provided the Creator with the model for decorating the whole world.“ Kepler considered the Harmonices Mundi his greatest work. The text relates his findings about the concept of congruence with respect to diverse categories of the physical domain: regularities in three-dimensional geometry, the relationships among different species of magnitude, the principles of consonance in music, and the organization of the Solar System. (“Spheres” as in the model of spheres renowed in the medieval era, in which the solar system and each planet was disposed in a separate sphere/orbit).

9 Chess Chess is said to have been created by a man who was asked by an indian Maharaja to find a way in which his son could have survived a war in which he previously fighted and died. The man asked to be rewarded with a grain of wheat for the first cell, two for the second, four for the third and so on, but the request would have been impossible to satisfy so it is said that: the Maharaja killed the man, or, instead gave him a kingdom to reward him.

10 Modern trivia and urban legends Jim Bumgardner created a stellar clock software based on the theory of the spheres of Kepler (http://wheelof.com/stars/)http://wheelof.com/stars/ It is said that the famous teorem of Fermat was demonstrated by himself in less than 2 lines. However no proof of this constatation was ever found. Numerology enthusiasts discovered a decagonal pattern in the world grid of meridians and parallels related to the golden ratio. The places where the edges of this hypotetical decagon are situated match with places like the bermuda triangle, the «witch well» in the norwegian sea and other sea places where is said that ships disappear. Eventual critics stated that the grid is a man invention thus impossible to relate to a natural pattern.. Similiar to the horus fractions there is the myth of A greatly different form of math today used is the Vedic math, a form of math discovered by Bharati Krishna Tirthaji Maharaja, in the 1900, extracted by the Vedas, sacred hindu texts, in which is used a special memorization technique since most of this mathematic is based on words and poems. Veda math has been renowed as a lot more creative and flexible than western math and can help early learning in childen.

11 This, and a lot else, are only a mere portion of what math has to tell us. Many other mysteries, as pyramides, Natza lines, the stories about Atlantis by Homer and his calendars, the mathematical model of the man-bird (the god of easter island population), Sumerian god and their involvment in the birth of math, the math of eastern philosophies, or also the strange stories about the great minds of our mind who revoluzioned math… Math evolves with the society, or the society evolves with math, but in the end its a single story that us humans are narrating throught different means which are the same: Music, Words, Math, Art. By Cosimo De Gregorio


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