Fractions~ Comparing, Equivalents and Number Lines | Math

Fractions~ Comparing, Equivalents and Number Lines

Fractions~ Comparing, Equivalents and Number Lines

MATHEMATIC HISTORY

Mathematics is among the oldest sciences in human history. In ancient times, Mathematics was defined as the science of numbers and shapes. Mathematics, like other branches of science, has evolved with time; it’s no further possible to explain it in a couple of sentences. What I’ve to express now will be words that emphasize its various aspects, as opposed to describe mathematics. In one aspect, mathematics is a skill like painting and music. A large proportion of mathematicians perform it as an art. Using this point of view, the fact a work done, a developed theory works in one way or another apart from mathematics does not concern them much. What matters to them may be the depth of the job done, the novelty of the strategy used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is a language. If the goal of science may be the universe; When it is to comprehend, rule and direct everything in the universe, we must manage to see 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. In order 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 see it as a game. Mathematics is only a tool for its user. After entering it, we understand and perceive what mathematics is in your knowledge and in the direction of our interest. Mathematics has become far beyond the dimensions any human can rule. Therefore, I don’t think that those who handle mathematics are far more than we understand and perceive it from mathematics compared to blind touched net understands and perceives the elephant. The phrase mathematics, for the very first time, BC. It had been employed by the members of the Pythagorean school in the 550s. His entry into the written literature, with Plato BC. It was in the 380s. The phrase meaning is “what needs to be learned”, that is, information. In the years before these dates, instead of the word mathematics, words which means that geometry, equivalent to it in geometry or old languages ​​were used.

It is difficult to say anything definite about where and how mathematics started. When we take documents that aren’t based on archaeological findings that require interpretation, but open enough to require interpretation, We can say so it started between 3000 and 2000 in Egypt and Mesopotamia. In accordance with Heredotus (485-415 BC), mathematics were only available in Egypt. You may already know, 97% of the Egyptian lands aren’t suited to agriculture; It is the 3% portion that gives life to Egypt and forms the Nile delta. Therefore, these lands are extremely valuable. However, at the conclusion of the floods caused by the Nile river every year, the boundaries of the landowners’lands become obscure. Because the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of their state, who’re responsible for these works, should come to take the mandatory measurements and give the landowners the maximum amount of land as they had in the earlier year. Herodotus says that geometry has begun to emerge consequently of the measurements and calculations. An additional opinion concerning the birth of mathematics is the one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics was born in Egypt. Nonetheless it was created out from the boredom of clergymen and priests, not the necessity for measurement-calculation due to Nile floods. At that time, the sole intellectual class of countries such as for example Egypt was the priest class. Considering that the livelihood of this class is provided by the general public or the state, they’ve much time for you to give intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of that point, in the same way others invented games like chess, bridge, and go&hellip ;.Both of these views might be true; priests wished to simplify the work of the geometric, or they found out just how to calculate the aspects of some geometric shapes such as for example triangular and trapezoidal to test that the distribution was fair, and this way led to the birth of geometry.

We shall divide the written history of mathematics into five periods. The very first period will soon 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, referred to as the Greek Mathematics period, between 500 years. The third term, M.S. It will cover a 1200-year period from the 500’s until the start 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 again to the early 1900s, called the age of modern mathematics, will be the fifth period. I will attempt to provide information regarding the development of mathematics in that period, contributing mathematicians, the area of mathematics in social life and the basic options that come with mathematics because period.

We shall start the initial 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. There are two main reasons for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The second reason could be the 3 big fires of the Alexandria libraries, the final of the fires happened during 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 create text instead of paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are based on the term papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it’s flaky due to moisture, heat and similar reasons. To date, two papyrus linked to mathematics appear to possess been hidden under exceptional circumstances. The key resources of our knowledge of Egyptian mathematics are those two papyri. The very first of the papyrus is really 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 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, following a few exercises given to show operations with fractional numbers, 87 questions are shown with their solutions. They are the sort of questions people can encounter in lifestyle, such as for instance sharing account, interest calculation, or finding the location of ​​some geometric shapes. This really is more or less our 8th grade mathematics. The next papyrus, referred to as the Moscow papyrus and now in the Moscow museum, can also be BC. It is really 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 may be the calculation of the volume and part of ​​the surface of the sphere part cut with a plane. Another is the question of finding the volume of a pyramid cut with a plane. Both questions were solved correctly. Both of these questions are accepted because the pinnacle of Egyptian mathematics. The Egyptians seen 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’s understood that Egyptian mathematics has remained as of this level for 2000 years and hasn’t made any significant progress.

B.C. 600s will be the years once the Persians started to dominate the center east. B.C. By the 550s, Persians are the only real 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, a year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 may be the date which was accepted as the start of Greek civilization. This date is the start of an extremely bright period in science, art and literature. Greek mathematics actually started earlier than this period. Two different people, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as the father of Greek mathematics. Tales Milet (Aydın) was also born. It is known 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 great pyramid by measuring along the shadow of the truly amazing pyramid, multiplying this number by the ratio of its length to the length of the current shadow. After time for Tales Milet, he taught them geometry by forming friends around him to teach what he learned. It’s assumed that abstract proof based on reasoning, which will be not centered on mathematics – experimental verification, entered into Tales. In addition, Tales is the person who is considered the very first philosopher in human history. He was created on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for a while, went to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken 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 school and tried to show individuals he gathered around. For political reasons, BC. He left 518 Samos, settled in southern Italy, in the town 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 next group consists of students attending school. Pythagoras school is founded on number cult. According in their mind, everything could 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 for instance 1,2,3,…; and kes, ¾,… will be the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem called the Pythagorean theorem (the square of the right sides of the right triangle equals the square of the hypotenuse) put the Pythagorean school in a heavy crisis. The discovery of irrational numbers is the very first major crisis of mathematics. Most of the members of the Pythagorean school were massacred by a raid led by way of 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 details, Egyptian and Mesopotamian mathematics are the basis of Greek mathematics.