Pythagoras and Early Pythagoreanism. Toronto: University of Toronto Press, Strohmeyer, John, and Peter Westbrook. Toggle navigation. Religious teachings Pythagoras and his followers were important for their contributions to both religion and science.
Mathematical teachings The Pythagoreans presented as fact the dualism that life is controlled by opposite forces between Limited and Unlimited. Cosmological views The Pythagoreans, as a result of their religious beliefs and careful study of mathematics, developed a cosmology dealing with the structures of the universe which differed in some important respects from the world views at the time, the most important of which was their view of the Earth as a sphere which circled the center of the universe.
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The data is also confusing regarding the family he formed. Some pointed out that he already had a wife and children before traveling to Crotona. In the same way, the information about the death of Pythagoras is quite ambiguous. In any case, the testimonies that some sources affirm that the year of b. Pythagoras, then 24 years later to b. It is believed, moreover, that he fled to Metaponto, and that here he was, according to the coincidence of several biographers, he lived his last days.
But other sources say that he returned to Crotona. The certain thing is that, while Cicero reigned, his tomb was exhibited in Metaponto. As if that were not enough, there are two versions of the reasons for his death.
The first one points out that, seeing the attack that he and his community had suffered, Pythagoras abandoned himself to his fate and died in the streets of Metaponto. However, having been rejected for not fulfilling the requirements, Matematikoi demanded, despite being a very rich man, swore to persecute Pythagoras and his followers in the place where they saw him. The Pythagorean society survived after Pythagoras , and by b. This led to problems in several cities, being in some cases persecuted and annihilated.
Finally, the society was divided into smaller groups according to the specific ideologies of each one. When inquiring into the history of the administration we must go back to the very needs of men to perform tasks in society.
Although some historians try to trace the origin of the administration to the development of the first commercial activities on the part of the Sumerians and Egyptians, it should be noted that planning, organizing, and directing workgroup activities were already present from much more remote times, s uch as the case of the Paleolithic hunters.
It was around these times that the history of administration was interwoven with the history of industrial engineering. As a result of the scientific school, the first five general principles of administration were considered:. Already in the 20th century, what is known as the tertiary sector, also called office work, rapidly developed, which led to a change of approach from the hitherto developed administrative theory. In , Henri Fayol divided business and industrial operations into six groups: technical, commercial, financial, security, accounting, and administration.
This division is considered the starting point of classical management school. Thus then the 14 principles of the classical management school were considered:.
In , the following contributions had influenced the development and consolidation of the Administration :. It is a competitive sport that runs several modalities. Most of the modalities demand the athlete to be balanced, strong, flexible, agile, resistant and composed.
Specifically, the most popular is rhythmic gymnastics. This sport was practiced in Rome, for the first time. Gymnastics also contained several modalities , such as walking, horse riding, and other gymnastic exercises. On some occasions, the loser in the competition was thrown into the Tiber.
Gymnastics also expanded in Greece, but more inclined to exercises in circuses, although later it was transformed into gladiatorial fights. The FIG has accepted six gymnastic modalities: artistic, rhythmic, trampoline, aerobic, acrobatic, and gymnastics for all. The first two are the most distinguished because they are part of the Summer Olympics. While, trampoline gymnastics has been part of the Olympic Games since , a competition that took place in Sydney. Artistic gymnastics: The gymnast performs a choreographic composition, in which he executes body movements at different speeds.
This modality contains several modalities according to the male and female categories. Rhythmic gymnastics: This modality combines elements of ballet, gymnastics, dance, and elements such as rope, hoop, ball, mallets, and ribbon can also be implemented.
This category has a level of competitions and another of exhibitions, music, and rhythm are very important when executing movements.
Rhythmic gymnastics can be performed individually and in groups. The score is over a maximum of 20 points. Trampoline gymnastics: In this discipline, a series of exercises are developed in various elastic devices, here acrobatics is the protagonist. Within this discipline, there are three specialties: tumbling, double mini-trampoline, and trampoline, the latter being part of the Olympic Games, since Aerobic gymnastics: It is known as sports aerobics, a routine of between and seconds is executed with high-intensity movements in addition to a series of elements of difficulty.
The gymnast must develop continuous movements, where he tests flexibility, strength, and perfect execution in the elements. Acrobatic gymnastics : It takes place in groups: male couple, female couple, mixed couple, female trio, and male quartet.
Collective gymnastic demonstrations are held, jumps, figures, and human pyramids are performed. Gymnastics for all: Gymnastics for everyone has some peculiarities; It is the only non-competitive gymnastics discipline endorsed by FIG. It can be performed by people of all ages and genders in groups from 6 to gymnasts who perform choreography in a synchronized way. It is divided into three categories: white, blue, and red groups.
The first is the basic category, the blue group is intermediate, and the red group the advanced. It is characteristic of general gymnastics to use uniform gymnastic elements and accessories to characterize a theme. This discipline may include dynamic activities and exercises from artistic, rhythmic, aerobic, acrobatic, trampoline, and dance gymnastics.
Coronaviruses are a group of common viruses that can affect the respiratory system, causing anything from a mild cold to pneumonia. It is commonly found in animals, but it can affect or be transmitted to humans. A new outbreak recently emerged, nCoV, causing the pneumonia epidemic in Wuhan China. To date, there are more than 30 species of the virus. They had no personal possessions and were vegetarians. Another group of followers who lived apart from the school were allowed to have personal possessions and were not expected to be vegetarians.
They all worked communally on discoveries and theories. Pythagoras believed:. Because of the strict secrecy among the members of Pythagoras' society, and the fact that they shared ideas and intellectual discoveries within the group and did not give individuals credit, it is difficult to be certain whether all the theorems attributed to Pythagoras were originally his, or whether they came from the communal society of the Pythagoreans.
Some of the students of Pythagoras eventually wrote down the theories, teachings and discoveries of the group, but the Pythagoreans always gave credit to Pythagoras as the Master for:. Pythagoras studied odd and even numbers, triangular numbers, and perfect numbers. Pythagoreans contributed to our understanding of angles, triangles, areas, proportion, polygons, and polyhedra.
As Aristotle wrote:- The Pythagorean This generalisation stemmed from Pythagoras's observations in music, mathematics and astronomy. Pythagoras noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments.
In fact Pythagoras made remarkable contributions to the mathematical theory of music. He was a fine musician, playing the lyre, and he used music as a means to help those who were ill. Pythagoras studied properties of numbers which would be familiar to mathematicians today, such as even and odd numbers, triangular numbers , perfect numbers etc.
However to Pythagoras numbers had personalities which we hardly recognise as mathematics today [ 3 ] :- Each number had its own personality - masculine or feminine, perfect or incomplete, beautiful or ugly. This feeling modern mathematics has deliberately eliminated, but we still find overtones of it in fiction and poetry. Of course today we particularly remember Pythagoras for his famous geometry theorem. Although the theorem, now known as Pythagoras's theorem, was known to the Babylonians years earlier he may have been the first to prove it.
Proclus , the last major Greek philosopher, who lived around AD wrote see [ 7 ] :- After [ Thales , etc. Again Proclus , writing of geometry, said:- I emulate the Pythagoreans who even had a conventional phrase to express what I mean "a figure and a platform, not a figure and a sixpence", by which they implied that the geometry which is deserving of study is that which, at each new theorem, sets up a platform to ascend by, and lifts the soul on high instead of allowing it to go down among the sensible objects and so become subservient to the common needs of this mortal life.
Heath [ 7 ] gives a list of theorems attributed to Pythagoras, or rather more generally to the Pythagoreans. We should note here that to Pythagoras the square on the hypotenuse would certainly not be thought of as a number multiplied by itself, but rather as a geometrical square constructed on the side. To say that the sum of two squares is equal to a third square meant that the two squares could be cut up and reassembled to form a square identical to the third square.
This is certainly attributed to the Pythagoreans but it does seem unlikely to have been due to Pythagoras himself. This went against Pythagoras's philosophy the all things are numbers, since by a number he meant the ratio of two whole numbers. However, because of his belief that all things are numbers it would be a natural task to try to prove that the hypotenuse of an isosceles right angled triangle had a length corresponding to a number.
It is thought that Pythagoras himself knew how to construct the first three but it is unlikely that he would have known how to construct the other two.
He also recognised that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realise that Venus as an evening star was the same planet as Venus as a morning star. References show. Biography in Encyclopaedia Britannica. M Cerchez, Pythagoras Romanian Bucharest, Diogenes Laertius, Lives of eminent philosophers New York, P Gorman, Pythagoras, a life C Byrne, The left-handed Pythagoras, Math. Intelligencer 12 3 , 52 -
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