After just a little searching, I found out the Pythagoras and his students had a significant impact on our mathematical knowledge!
He was born on Samos, a Greek island in the Aegean Sea that is very close to the west coast of Turkey 580 B.C.
A major belief of his is "All is number". This means that numbers did not just exist as an abstraction or thought in the human mind BUT had a reality all their own that did not depend on one's mind. It meant that numbers and relations between numbers formed the basic core out of which everything else came. "Numbers were to Pythagoreus and his followers what atoms are to the human race today.
Can you find information about Pythagoras and his findings about music??
When I post questions, you may post answers for extra credit!!!
Did you know Pythagoras founded the Order of the Pythagoreans? almost like a religion or cult? Can you tell me more?
What other contributions to mathematics are attributed to Pythagoras and his followers?
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Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy, and the theory of music. The theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier but he may have been the first to prove it.
These are some quotations by Pythegoras:
"Every man has been made by God in order to acquire knowledge and contemplate."
"Geometry is knowledge of the eternally existent."
"Number is the within of all things."
"There is geometry in the humming of the strings."
"Time is the soul of this world."
Pathagoras born on c. 580 BC, Samos, Ionia, Greece and died c. 500, Metapontum, Lucania,Greece.
He migrated to southern Italy about 532 BC, apparently to escape Samos's tyrannical rule, and established his ethico-political academy at Croton (now Crotone).
Pathagoras 's facts:
Cause of death: unspecified
Gender: Male
Religion: Cult
Race or Ethnicity: White
Sexual orientation: Straight
Occupation: Mathematician, Philosopher, Religion
Nationality: Ancient Greece
Executive summary: Pythagorean Theorem
Pythagorean Mathematics
One point: generator of dimensions.
Two points: generator of a line of dimension one
Three points: generator of a triangle of dimension two
Four points: generator of a tetrahedron, of dimension three.
The sum of these is ten and represents all dimensions. Note the abstraction of concept. This is a distance from ``fingers and toes".
Classification of numbers:
The distinction between even and odd numbers certainly dates to Pythagoras;"...number is of two special kinds, odd and even, with a third, even-odd, arising from a mixture of the two; and of each kind there are many forms." This is, even and odd, correspond to the usual definitions. However, even-odd means a product of an even and odd number. Note: orginally the number 2 was not considered even.
Prime or incomposite numbers and secondary or composite numbers:
A prime number is rectilinear, meaning that it can only be set out in one dimension. The number 2 was not originally regarded as a prime number, or even as a number at all.
A composite number is that which is measured by some number. (Euclid)
Two numbers are prime to one another or composite to one another if their greatest common divisor is one or greater than one, respectively.
Contributions by the Pythagoreans include
Various theorems about triangles, parallel lines, polygons, circles, spheres and regular polyhedra.
Work on a class of problems in the applications of areas. (e.g. to construct a polygon of given area and similar to another polygon.)
Given a line segment, construct on part of it or on the line segment extended a parallelogram equal to a given rectilinear figure in area and falling short or exceeding by a parallelogram similar to a given one. (In modern terms, solve .)
Mathematician Pythagoras founded a religious sect that believed the whole world could be explained and described by whole numbers. For example, he noted that dividing a vibrating string into lengths determined by whole number ratios could make beautiful sounds. The harmonics he developed were crucial to his view of the natural world.He believed that the planets moved in circular orbits, and that the mathematics of this celestial motion was so beautiful that the planets actually made music as they traversed their heavenly course. If you were to ask Pythagoras why we do not hear the music, he would reply that because you have been hearing this "music of the spheres" since you were born, you don't realize that you are listening to it. In essence, you have never heard silence. Pythagoras also believed in the transmigration of souls. As a result, he was strict a vegetarian and respected animals. The belief in the transmigration of souls also caused him to regard men and women as equals and to treat slaves humanely.
PYTHAGOREAN THEOREM'S ORIGIN:
In spite of its name, the Pythagorean theorem was not discovered by Pythagoras. The earliest known formulation of the theorem was written down by the Indian mathematician Baudhāyana in 800BC. The principle was also known to the earlier Egyptian and the Babylonian master builders. However, Pythagoras may have proved the theorem and popularised it in the Greek world. With it, his name and his philosophy have survived the turbulences of history.
The Pythagorean theorem is often cited as the beginning of mathematics in Western culture, and ever since mathematics -the art of demonstrative and deductive reasoning- has had a profound influence on Western philosophy, which can be observed down to Russell and Wittgenstein.
Great job on the blog Mrs. Tucker. Well, I did a mini research on Pythagoras and his findings of music. In the 6th century BC Pythagoras discovered 'musical notes' by observing a blacksmith. Pythagoras noticed when the blacksmith struck his anvil the different 'notes' were produced depending on the anvils weight. Pythagoras was also said to be the first to discover the consonant acoustic relationship between strings of proportional length. If the strings are proportion and equal in tension, they will produce the same tone when plucked. The tone will be the same regardless of material difference in the string.
[Amy Tran Period 1]
This is what I found on Pythagoras and his music backround. Pythagoras observed that when the blacksmith struck his anvil, different notes were produced according to the weight of the hammer.
Pythagoras’ religious and scientific views were, in his opinion, inseparably interconnected. However, they are looked at separately in the 21st century. Religiously, Pythagoras was a believer of metempsychosis. He believed in transmigration, or the reincarnation of the soul again and again into the bodies of humans, animals, or vegetables until it became moral. His ideas of reincarnation were influenced by Greek Mythology. He was one of the first to propose that the thought processes and the soul were located in the brain and not the heart. He himself claimed to have lived four lives that he could remember in detail, and heard the cry of his dead friend in the bark of a dog.
One of Pythagoras' beliefs was that the essence of being is number. Thus, being relies on stability of all things that create the universe. Things like health relied on a stable proportion of elements; too much or too little of one thing causes an imbalance that makes a being unhealthy. Pythagoras viewed thinking as the calculating with the idea numbers. When combined with the Folk theories, the philosophy evolves into a belief that Knowledge of the essence of being can be found in the form of numbers. If this is taken a step further, one can say that because mathematics is an unseen essence, the essence of being is an unseen characteristic that can be encountered by the study of mathematics.
Pythagoras is commonly given credit for discovering the Pythagorean theorem, a theorem in trigonometry that states that in a right-angled triangle the square of the hypotenuse (the side opposite the right angle), c, is equal to the sum of the squares of the other two sides, b and a—that is, a² + b² = c².
While the theorem that now bears his name was known and previously utilized by the Babylonians, and Indians, he, or his students, are thought to have constructed the first proof. Because of the secretive nature of his school and the custom of its students to attribute everything to their teacher, there is no evidence that Pythagoras himself worked on or proved this theorem. For that matter, there is no evidence that he worked on any mathematical or meta-mathematical problems. Some attribute it as a carefully constructed myth by followers of Plato over two centuries after the death of Pythagoras, mainly to bolster the case for Platonic meta-physics, which resonate well with the ideas they attributed to Pythagoras. This attribution has stuck, down the centuries up to modern times. [5] The earliest known mention of Pythagoras's name in connection with the theorem occurred five centuries after his death, in the writings of Cicero and Plutarch.
Today, Pythagoras is revered as a prophet by the Ahl al-Tawhid or Druze faith along with his fellow Greek, Plato.
According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when one day he passed blacksmiths at work, and thought that the sounds emanating from their anvils being hit were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths to learn how this had happened by looking at their tools, he discovered that it was because the anvils were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on." (See Pythagorean tuning.)
The Pythagoreans elaborated on a theory of numbers, the exact meaning of which is still debated among scholars. Pythagoras believed in something called the harmony of the spheres. He believed that the planets and stars moved according to mathematical equations, which corresponded to musical notes and thus produced a symphony.[6]
Obviously he and his followers came up with the Pythagorean theorem, but they also are credited with finding the degree sum in polygons, which is what we are learning right now. 180(n-2)then all of that divided by number of sides.
He also figured that the sum of exterior angles equals 360 on all polygons.
He also figured out that the farther away a planet is away from us the slower its orbital period is longer.
He did make mistakes though. He thought that the earth was the center of the universe
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