Fundamentals booklets and activities 1 and 2: BREAKING HEAD FOR SEQUIN STUDY … | Math

Fundamentals booklets and activities 1 and 2: BREAKING HEAD FOR SEQUIN STUDY …

Fundamental booklets and activities 1 and 2: BREAKING HEAD FOR SEQUENCES-#math #gcse

MATHEMATIC HISTORY

Mathematics is one of many oldest sciences in human history. In ancient times, Mathematics was defined whilst the science of numbers and shapes. Mathematics, like other branches of science, has evolved as time passes; it is no further possible to explain it in a few sentences. What I’ve to say now is going to be words that emphasize its various aspects, as opposed to describe mathematics. In taking care of, mathematics is a skill like painting and music. The great majority of mathematicians perform it as an art. Out of this perspective, the fact a work done, a developed theory works in one of the ways or another apart from mathematics doesn’t concern them much. What matters for them is the depth of the task 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 objective of science is the universe; If it is to understand, rule and direct everything in the universe, we must be able 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. In order to understand and interpret them, we need to know the language of mathematics. In another aspect, mathematics is an intellectual game like chess.

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

It’s extremely hard to state anything definite about where and how mathematics started. If we take documents that are not centered on archaeological findings that require interpretation, but open enough to require interpretation, We are able to say so 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’s the 3% portion that gives life to Egypt and forms the Nile delta. Therefore, these lands are really valuable. However, at the conclusion of the floods caused by the Nile river every year, 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 their state, who’re responsible for these works, should arrive at take the required measurements and provide the landowners as much land as they had in the earlier year. Herodotus says that geometry has begun to emerge as a result of those measurements and calculations. An additional opinion in regards to the birth of mathematics is usually the one put forward by Aristotle (384-322 BC). In accordance with Aristotle, mathematics was created in Egypt. Nonetheless it was born out of the boredom of clergymen and priests, not the need for measurement-calculation brought on by Nile floods. In those days, the only intellectual class of countries such as Egypt was the priest class. Considering that the livelihood of the class is supplied by people or their state, they’ve much time for you to give to intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of that time, just like 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 to calculate the regions of some geometric shapes such as triangular and trapezoidal to test that the distribution was fair, and this way resulted in the birth of geometry.

We will divide the written history of mathematics into five periods. The initial period will be Egypt and Mesopotamia; this period BC In 2000s BC. It’ll cover a period of 1500-2000 years between 500s. The next period, BC. 500-M.S. It’ll 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 residing in, dating back again to the early 1900s, called the age of modern mathematics, could be the fifth period. I will endeavour to offer information about the development of mathematics for the reason that period, contributing mathematicians, the place of mathematics in social life and the essential options that come with mathematics in that 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 first is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason may be the 3 big fires of the Alexandria libraries, the final of those fires happened through the conquest of Egypt by 641 Muslims, the written documents disappeared. Papyrus may 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 publish text instead of paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are derived from the phrase papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it’s flaky because of moisture, heat and similar reasons. To date, two papyrus related to mathematics appear to have been hidden under exceptional circumstances. The main sources of our understanding of Egyptian mathematics are these two papyri. The initial of these 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 teach math. In the introduction part, following a few exercises given to instruct operations with fractional numbers, 87 questions receive with their solutions. They are the kind of questions people can encounter in daily life, such as sharing account, interest calculation, or finding the region of ​​some geometric shapes. This really is just about our 8th grade mathematics. The 2nd papyrus, known as 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 kind of questions in the Ahmes papyrus, except for the two. Are you aware that other two questions, one could be the calculation of the volume and section of ​​the surface of the sphere part cut by a plane. Another may be the question of finding the quantity of a pyramid cut by a plane. Both questions were solved correctly. Those two questions are accepted because the pinnacle of Egyptian mathematics. The Egyptians realized that the area of ​​the circle was proportional to its diameter and found the number 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 has not made any significant progress.

B.C. 600s will be the years once the Persians began 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, a year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 could be the date that has been accepted as the beginning of Greek civilization. This date is the beginning of a very bright period in science, art and literature. Greek mathematics actually started prior to when this period. Two different people, Tales (624-547 BC) and Pythagoras (569-475 BC), are considered to be the father of Greek mathematics. Tales Milet (Aydın) was also born. It is known that he visited Egypt, stayed there for a time and learned geometry in Egypt. During Egypt, it is described in books where he calculates the height of the fantastic pyramid by measuring the length of the shadow of the great pyramid, multiplying this number by the ratio of its length to the size of the current shadow. After returning to Tales Milet, he taught them geometry by forming an organization around him to show what he learned. It is assumed that abstract proof based on reasoning, that will be not centered on mathematics – experimental verification, entered into Tales. In addition, Tales is the person who is recognized as the very first philosopher in human history. He came to be 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 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 school and tried to show the folks 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 are connected to one another 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 comes with 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,… would 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 best 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 initial major crisis of mathematics. Lots of the members of the Pythagorean school were massacred by 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 can be understood from this information, Egyptian and Mesopotamian mathematics are the basis of Greek mathematics.

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