Fractions | Math

Fractions

Fractions

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’s no longer possible to describe it in a few sentences. What I’ve to state now is likely to be words that emphasize its various aspects, as opposed to describe mathematics. In taking care of, mathematics is an art form like painting and music. The vast majority 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 for them is the depth of the work done, the novelty of the methods used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really a language. If the objective of science is the universe; If it is to comprehend, rule and direct everything in the universe, we should have the ability to browse 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 must know the language of mathematics. In another aspect, mathematics is an intellectual game like chess.

Some mathematicians also see it as a game. Mathematics is merely a tool because of its user. After entering it, we understand and perceive what mathematics is in your 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 cope with 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 word mathematics, for the first time, BC. It absolutely was utilized by the members of the Pythagorean school in the 550s. His entry to the written literature, with Plato BC. It absolutely was in the 380s. The term meaning is “what must be learned”, that’s, information. In the years before these dates, rather than the word mathematics, words which means that geometry, comparable to it in geometry or old languages ​​were used.

It is difficult to say anything definite about where and how mathematics started. If we take documents that aren’t centered on archaeological findings that need interpretation, but open enough to require interpretation, We are able to say so it started between 3000 and 2000 in Egypt and Mesopotamia. Based on Heredotus (485-415 BC), mathematics started in Egypt. You may already know, 97% of the Egyptian lands are not suitable for agriculture; It is the 3% portion that provides life to Egypt and forms the Nile delta. Therefore, these lands are incredibly valuable. However, by the end of the floods caused by the Nile river annually, the boundaries of the landowners’lands become obscure. Because the landowners also pay taxes in proportion to the land they own, after every flood, the “geometricists” of their state, who are responsible for these works, should come to take the necessary measurements and provide the landowners just as much land as they had in the last year. Herodotus says that geometry has begun to emerge as a result of those measurements and calculations. A second opinion about the birth of mathematics is usually the one put forward by Aristotle (384-322 BC). Based on Aristotle, mathematics came to be in Egypt. Nonetheless it was created out from the boredom of clergymen and priests, not the requirement for measurement-calculation due to Nile floods. In those days, the sole intellectual class of countries such as for example Egypt was the priest class. Because the livelihood of the class is given by people 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 the period, in the same way others invented games like chess, bridge, and go&hellip ;.Both of these views may be true; priests wanted to simplify the work of the geometric, or they learned just how to calculate the regions of some geometric shapes such as for example triangular and trapezoidal to test that the distribution was fair, and in this manner led to 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’ll cover an amount of 1500-2000 years between 500s. The next period, BC. 500-M.S. It’ll cover an amount of 1000 years, called the Greek Mathematics period, between 500 years. The third term, M.S. It’ll 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 scale we are surviving in, dating back again to the first 1900s, called age modern mathematics, will be the fifth period. I will endeavour to offer information about the development of mathematics because period, contributing mathematicians, the area of mathematics in social life and the essential top features of 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 major causes for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason could be the 3 big fires of the Alexandria libraries, the last 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, typically 15-25 meters long and 30-50 inches wide. These leaves were used to create text rather than paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are derived from the word papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it’s flaky because of moisture, heat and similar reasons. Up to now, two papyrus linked to mathematics appear to possess been hidden under exceptional circumstances. The main sourced elements of our knowledge of Egyptian mathematics are both of these papyri. The first of these papyrus is really a 6-meter long and 35-cm wide papyrus known as the Ahmes (or Rhind) papyrus. This papyrus, BC. You are a puree written in 2000s, BC. It is just a copy written 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 book written to teach math. In the introduction part, after having a few exercises given to instruct operations with fractional numbers, 87 questions receive with their solutions. These are the type of questions people can encounter in daily life, such as for instance sharing account, interest calculation, or finding the region of ​​some geometric shapes. This 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 just a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the sort of questions in the Ahmes papyrus, with the exception of the two. When it comes to other two questions, one of them is the calculation of the volume and area of ​​the surface of the sphere part cut with a plane. Another could be the question of finding the volume of a pyramid cut by way of a plane. Both questions were solved correctly. Those two questions are accepted while the pinnacle of Egyptian mathematics. The Egyptians seen that the area 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 at this level for 2000 years and has not made any significant progress.

B.C. 600s would be the years when the Persians started 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 may be the date which was accepted as the beginning of Greek civilization. This date is the start of a very bright period in science, art and literature. Greek mathematics actually started sooner than this period. Two different people, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as being the daddy of Greek mathematics. Tales Milet (Aydın) was also born. It is known that he visited Egypt, stayed there for some time and learned geometry in Egypt. Whilst in Egypt, it is described in books where he calculates the height of the truly amazing pyramid by measuring the length of the shadow of the truly amazing pyramid, multiplying this number by the ratio of its length to along the current shadow. After time for Tales Milet, he taught them geometry by forming a group 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 recognized as the first philosopher in human history. He was born 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 up to Babylon by capturing the Persians during 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 returning to Samos, he created a college and tried to teach the people 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 are connected to each other with oath. The 2nd group consists of students attending school. Pythagoras school is dependant on number cult. According to them, everything can be reduced to numbers; It posseses an unusually perfect harmony among numbers, and harmony is 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,… are 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 proper sides of a right triangle equals the square of the hypotenuse) put the Pythagorean school in a heavy crisis. The discovery of irrational numbers is the initial major crisis of mathematics. Many of the members of the Pythagorean school were massacred by way of a raid led by way of a big cyber named Cylon. Pythagoras saved his life, but after a couple of years he died. Pythagoras’thoughts, the Pythagorean school lived for many years under this or that name. As may be understood from these records, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.