Booklets and fundamental activities 1 and 2: BREAKING THE HEAD FOR SEQUENCES STUDY … | Math

Booklets and fundamental activities 1 and 2: BREAKING THE HEAD FOR SEQUENCES STUDY …

Booklets and fundamental activities 1 and 2: HEADBAND FOR NUMBER SEQUENCE STUDY

MATHEMATIC HISTORY

Mathematics is among the oldest sciences in human history. In ancient times, Mathematics was defined while the science of numbers and shapes. Mathematics, like other branches of science, has evolved as time passes; it’s no further possible to describe it in a few sentences. What I’ve to state now will be words that emphasize its various aspects, as opposed to describe mathematics. In taking care of, mathematics is a skill like painting and music. A large proportion of mathematicians perform it as an art. From this standpoint, 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 for them 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 purpose of science is the universe; If it is to understand, rule and direct everything in the universe, we must manage 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 can be an intellectual game like chess.

Some mathematicians also view it as a game. Mathematics is merely a tool for the user. After entering it, we understand and perceive what mathematics is in your knowledge and in the direction of our interest. Mathematics is currently far beyond the dimensions any human can rule. Therefore, I do not think that people who deal with mathematics are far more than we understand and perceive it from mathematics compared to blind touched net understands and perceives the elephant. The word mathematics, for the first time, BC. It had been 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 needs to be learned”, that’s, information. In the years before these dates, rather than the word mathematics, words that mean geometry, equal 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 based on archaeological findings that require interpretation, but open enough to require interpretation, We can say that 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 are not ideal for agriculture; It’s the 3% portion that gives life to Egypt and forms the Nile delta. Therefore, these lands are extremely valuable. However, at the end of the floods caused by the Nile river annually, the boundaries of the landowners’lands become obscure. Since the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of the state, that are in charge of these works, should arrived at take the mandatory measurements and supply the landowners as much land as they had in the previous year. Herodotus says that geometry has begun to emerge as a result of those measurements and calculations. An additional 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. Nonetheless it was born out from the boredom of clergymen and priests, not the requirement for measurement-calculation due to Nile floods. In those days, the only intellectual class of countries such as for example Egypt was the priest class. Since the livelihood of the class is provided by people or their state, they’ve much time and energy to give intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of the period, just as others invented games like chess, bridge, and go&hellip ;.Both these views may be true; priests desired to simplify the task of the geometric, or they discovered how exactly to calculate the areas of some geometric shapes such as for example triangular and trapezoidal to check 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 2nd period, BC. 500-M.S. It’ll cover a period of 1000 years, called 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, referred to as the golden age of mathematics, dating from 1700-1900. The period we’re living in, dating back once again to early 1900s, called age modern mathematics, would be the fifth period. I will attempt to offer information about the development of mathematics because period, contributing mathematicians, the area of mathematics in social life and the basic top features of mathematics because period.

We will 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 will find two main reasons for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The second reason is 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, typically 15-25 meters long and 30-50 inches wide. These leaves were used to write text rather than paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are based on the word papyrus. The typical lifespan of a papyrus is 300 years; 300 years later, it is flaky because of moisture, heat and similar reasons. Currently, two papyrus linked to mathematics appear to own been hidden under exceptional circumstances. The main sources of our knowledge of Egyptian mathematics are both of these papyri. The first of the papyrus is 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 really 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 show math. In the introduction part, after a few exercises given to teach operations with fractional numbers, 87 questions are given with their solutions. They’re the type of questions people can encounter in lifestyle, such as sharing account, interest calculation, or finding the location of ​​some geometric shapes. That is just about our 8th grade mathematics. The second papyrus, called the Moscow papyrus and now in the Moscow museum, can be BC. It is a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the type of questions in the Ahmes papyrus, with the exception of the two. Are you aware that other two questions, one is the calculation of the amount and area of ​​the surface of the sphere part cut by way of a plane. One other is the question of finding the volume of a pyramid cut by a plane. Both questions were solved correctly. These two questions are accepted whilst the pinnacle of Egyptian mathematics. The Egyptians realized that the area of ​​the circle was proportional to its diameter and found how many pi to be 4x (8/9) squared, ie 256/81 = 3.16. It’s understood that Egyptian mathematics has remained only at that level for 2000 years and has not made any significant progress.

B.C. 600s are the years once the Persians started initially to dominate the center 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, annually 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 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 considered to be the daddy of Greek mathematics. Tales Milet (Aydın) was also born. It is famous he visited Egypt, stayed there for a time and learned geometry in Egypt. Whilst in Egypt, it’s described in books where he calculates the height of the truly amazing pyramid by measuring the size of 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 instruct what he learned. It is assumed that abstract proof centered on reasoning, which can be not centered on mathematics – experimental verification, entered into Tales. Additionally, Tales is the person who is known as the 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 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 through 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 teach 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 people of this school called “mathematics” live together and they’re connected to each other with oath. The second group includes students attending school. Pythagoras school is based on number cult. According to them, everything may be reduced to numbers; It has 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,… are the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem referred to 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 initial major crisis of mathematics. Most of the members of the Pythagorean school were massacred by way of a raid led with a big cyber named Cylon. Pythagoras saved his life, but after a couple of years he died. Pythagoras’thoughts, the Pythagorean school lived for several years under this or that name. As may be understood from these details, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.

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