Off the Number Line: Birth of a Right Triangle | Math

Off the Number Line: Birth of a Right Triangle

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MATHEMATIC HISTORY

Mathematics is among the oldest sciences in human history. In ancient times, Mathematics was defined because the science of numbers and shapes. Mathematics, like other branches of science, has evolved as time passes; it is no longer possible to describe it in several sentences. What I’ve to say now is likely to be words that emphasize its various aspects, as opposed to describe mathematics. In taking care of, mathematics is an art like painting and music. The great majority of mathematicians perform it as an art. Using this viewpoint, the fact that a work done, a developed theory works in one of the ways or another other than mathematics doesn’t concern them much. What matters in their mind is the depth of the work done, the novelty of the techniques used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really a language. If the goal of science could be the universe; When it is to comprehend, rule and direct everything in the universe, we must manage to read the book of nature. The book of nature is written in the language of mathematics, with the highly cited words of Galile; its letters are shapes of geometry. To be able to understand and interpret them, we have to know the language of mathematics. In another aspect, mathematics can be an intellectual game like chess.

Some mathematicians also view it as a game. Mathematics is just a tool because of its user. After entering it, we understand and perceive what mathematics is inside our knowledge and in the direction of our interest. Mathematics is now far beyond the dimensions any human can rule. Therefore, I do not believe those who handle mathematics tend to be more than we understand and perceive it from mathematics compared to the blind touched net understands and perceives the elephant. The term mathematics, for the first time, BC. It absolutely was employed by the members of the Pythagorean school in the 550s. His entry in to the written literature, with Plato BC. It was in the 380s. The term meaning is “what must be learned”, that is, information. In the years before these dates, as opposed to the word mathematics, words that mean geometry, equivalent to it in geometry or old languages ​​were used.

It is difficult to express anything definite about where and how mathematics started. If we take documents which are not centered on archaeological findings that need interpretation, but open enough to require interpretation, We are able to say that it started between 3000 and 2000 in Egypt and Mesopotamia. According to Heredotus (485-415 BC), mathematics started in Egypt. Everbody knows, 97% of the Egyptian lands aren’t suitable for agriculture; It is the 3% portion that offers life to Egypt and forms the Nile delta. Therefore, these lands are really valuable. However, at the conclusion of the floods brought on by the Nile river each year, the boundaries of the landowners’lands become obscure. Since the landowners also pay taxes in proportion to the land they own, after each flood, the “geometricists” of their state, who’re in charge of these works, should arrived at take the necessary measurements and supply the landowners the maximum amount of land as they’d in the earlier year. Herodotus says that geometry has begun to emerge consequently of these measurements and calculations. Another opinion about the birth of mathematics is usually the one put forward by Aristotle (384-322 BC). Based on Aristotle, mathematics was created in Egypt. But it was born from the boredom of clergymen and priests, not the requirement for measurement-calculation caused by Nile floods. In those days, the sole intellectual class of countries such as for example Egypt was the priest class. Since the livelihood of this class is supplied by the public or their state, they’ve much time and energy to share with intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of the period, just as others invented games like chess, bridge, and go&hellip ;.These two views might be true; priests wished to simplify the job of the geometric, or they found out how to calculate the aspects of some geometric shapes such as triangular and trapezoidal to check on that the distribution was fair, and in this manner generated the birth of geometry.

We will divide the written history of mathematics into five periods. The initial period is going to be Egypt and Mesopotamia; this period BC In 2000s BC. It will cover an amount of 1500-2000 years between 500s. The second period, BC. 500-M.S. It will cover a period of 1000 years, known as the Greek Mathematics period, between 500 years. The 3rd term, M.S. It will cover a 1200-year period from the 500’s until the beginning of calculus and will mainly cover European mathematics in the Hind, Islam and Renaissance era. The fourth semester will cover the classical mathematics era, called the golden age of mathematics, dating from 1700-1900. The time we’re living in, dating back once again to the first 1900s, called the age of modern mathematics, would be the fifth period. I will try to provide information regarding the development of mathematics for the reason that period, contributing mathematicians, the spot of mathematics in social life and the fundamental features of mathematics in that period.

We shall start the first semester with Egyptian mathematics. Written documents about ancient Egyptian mathematics and generally Egyptian history – I don’t mean the remains of archaeological works – are almost nonexistent. You can find two significant reasons for this. The first is that the ancient Egyptians wrote the writing on papyrus; The next reason could be the 3 big fires of the Alexandria libraries, the final of the fires happened throughout the conquest of Egypt by 641 Muslims, the written documents disappeared. Papyrus could be the leaves of a reddish, reed type plant growing in the Nile delta, an average of 15-25 meters long and 30-50 inches wide. These leaves were used to publish text in place of paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are based on the phrase papyrus. The typical lifespan of a papyrus is 300 years; 300 years later, it is flaky due to moisture, heat and similar reasons. Currently, two papyrus related to mathematics appear to have been hidden under exceptional circumstances. The main sourced elements of our knowledge of Egyptian mathematics are these two papyri. The very first of the papyrus is a 6-meter long and 35-cm wide papyrus called the Ahmes (or Rhind) papyrus. This papyrus, BC. You are a puree written in 2000s, BC. It is just a copy published by a “mathematician” named Ahmes in the 1650s. This papyrus was bought by the Irish antiquarian H. Rhind in the 1850s, now in the British museum. This papyrus is a guide written to show math. In the introduction part, after a few exercises given to instruct operations with fractional numbers, 87 questions are made with their solutions. They are the sort of questions people can encounter in daily life, such as for example sharing account, interest calculation, or finding the area of ​​some geometric shapes. That is just about our 8th grade mathematics. The second papyrus, referred to as the Moscow papyrus and now in the Moscow museum, is also BC. It is just a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the kind of questions in the Ahmes papyrus, aside from the two. Are you aware that other two questions, one could be the calculation of the amount and section of ​​the surface of the sphere part cut with a plane. Another could be the question of finding the quantity of a pyramid cut by a plane. Both questions were solved correctly. Those two questions are accepted whilst the pinnacle of Egyptian mathematics. The Egyptians realized that the location of ​​the circle was proportional to its diameter and found the amount of pi to be 4x (8/9) squared, ie 256/81 = 3.16. It is understood that Egyptian mathematics has remained only at that level for 2000 years and hasn’t made any significant progress.

B.C. 600s are the years once the Persians started initially to dominate the middle east. B.C. By the 550s, Persians are the sole rulers of the entire middle east, including Anatolia and Egypt. The Persians organize three trips to Greece between 500-480 BC; They captured Athens in 480, but burned it, per year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 is the date that was accepted as the beginning of Greek civilization. This date is the start of a really bright period in science, art and literature. Greek mathematics actually started prior to when this period. A couple, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as being the father of Greek mathematics. Tales Milet (Aydın) was also born. It is famous that he went along to Egypt, stayed there for a while and learned geometry in Egypt. Whilst in Egypt, it is described in books where he calculates the height of the fantastic pyramid by measuring along the shadow of the great pyramid, multiplying this number by the ratio of its length to the length of the present shadow. After returning to Tales Milet, he taught them geometry by forming an organization around him to teach what he learned. It’s assumed that abstract proof predicated on reasoning, which can be not based on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the one who is recognized as the initial philosopher in human history. He was created on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for some time, went to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken fully to Babylon by capturing the Persians throughout the occupation of Egypt by the Persians. it is known. During his 5 years in Babylon, he learned mathematics, music and religious information, and after time for Samos, he created a college and tried to instruct the people he gathered around. For political reasons, BC. He left 518 Samos, settled in southern Italy, in the city of Crotone, where he created a semi-mystical-semi-scientific, cult-like school. The senior folks of this school called “mathematics” live together and they’re connected together with oath. The 2nd group contains students attending school. Pythagoras school is founded on number cult. According for them, everything may be reduced to numbers; It posseses an unusually perfect harmony among numbers, and harmony is really a reflection of the divine harmony. Known numbers for that day are integers indicating the plurality such as 1,2,3,…; and kes, ¾,… would be the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem known as the Pythagorean theorem (the square of the best sides of a right triangle equals the square of the hypotenuse) put the Pythagorean school in a strong crisis. The discovery of irrational numbers is the first major crisis of mathematics. Many of the members of the Pythagorean school were massacred with a raid led with a big cyber named Cylon. Pythagoras saved his life, but after a few years he died. Pythagoras’thoughts, the Pythagorean school lived for many years under this or that name. As can be understood from these records, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.

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