Interactive Notebook Setup | Math

Interactive Notebook Setup

Math Study Tips for an Interactive Notebook

MATHEMATIC HISTORY

Mathematics is one of 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 longer possible to describe it in a couple of sentences. What I’ve to express now will undoubtedly be words that emphasize its various aspects, rather than describe mathematics. In taking care of, mathematics is a skill like painting and music. A large proportion of mathematicians perform it being an art. Out of this perspective, the fact a work done, a developed theory works in one way or another apart from mathematics doesn’t concern them much. What matters in their mind is the depth of the job done, the novelty of the techniques used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is just a language. If the goal of science may be the universe; When it is to understand, rule and direct everything in the universe, we ought to have the ability 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 must 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 merely a tool for its user. After entering it, we understand and perceive what mathematics is within our knowledge and in the direction of our interest. Mathematics has become far beyond the dimensions any human can rule. Therefore, I don’t believe that those who deal with mathematics are more than we understand and perceive it from mathematics than the blind touched net understands and perceives the elephant. The phrase 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 absolutely was in the 380s. The phrase meaning is “what needs to be learned”, that is, 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’s difficult to state anything definite about where and how mathematics started. When we take documents that aren’t centered on archaeological findings that need interpretation, but open enough to require interpretation, We can say that it started between 3000 and 2000 in Egypt and Mesopotamia. According to Heredotus (485-415 BC), mathematics were only available in Egypt. Everbody knows, 97% of the Egyptian lands are not suitable for agriculture; It is the 3% portion that offers 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 each flood, the “geometricists” of the state, who are accountable for these works, should arrived at take the required measurements and provide the landowners the maximum amount of land as they had in the previous year. Herodotus says that geometry has begun to emerge as a result of the measurements and calculations. An additional opinion concerning the birth of mathematics is the main one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics came to be in Egypt. Nonetheless it was created out of the boredom of clergymen and priests, not the necessity for measurement-calculation brought on by Nile floods. In those days, the sole intellectual class of countries such as Egypt was the priest class. Because the livelihood with this class is supplied by the general public or the state, they have much time for you to share with intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of that time, in the same way others invented games like chess, bridge, and go&hellip ;.These two views might be true; priests wanted to simplify the task of the geometric, or they discovered just how to calculate the regions of some geometric shapes such as triangular and trapezoidal to check that the distribution was fair, and in this way generated the birth of geometry.

We shall divide the written history of mathematics into five periods. The initial period will undoubtedly 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’ll cover an amount of 1000 years, referred to as the Greek Mathematics period, between 500 years. The 3rd term, M.S. It’ll 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, known as the golden age of mathematics, dating from 1700-1900. The period we are residing in, dating back again to early 1900s, called age modern mathematics, could be the fifth period. I will try to offer information regarding the development of mathematics in that period, contributing mathematicians, the area of mathematics in social life and the fundamental options that come with mathematics because 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. There are two significant reasons for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The second reason may be the 3 big fires of the Alexandria libraries, the final of these 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, normally 15-25 meters long and 30-50 inches wide. These leaves were used to publish text rather than paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are produced from the phrase papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it’s flaky due to moisture, heat and similar reasons. Currently, two papyrus related to mathematics appear to possess been hidden under exceptional circumstances. The key sources of our knowledge of Egyptian mathematics are these two papyri. The initial of these papyrus is really a 6-meter long and 35-cm wide papyrus referred to as 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 instruct math. In the introduction part, after having a few exercises given to teach operations with fractional numbers, 87 questions are shown using 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 area of ​​some geometric shapes. That is pretty much 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, with the exception of the two. As for the other two questions, one may be the calculation of the quantity and area of ​​the surface of the sphere part cut by way of a plane. The other is 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 since the pinnacle of Egyptian mathematics. The Egyptians seen 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 is understood that Egyptian mathematics has remained only at that level for 2000 years and hasn’t made any significant progress.

B.C. 600s will be the years when 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, annually later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 may be the date that was accepted as the beginning 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 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 known he went along to Egypt, stayed there for a while and learned geometry in Egypt. During 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 great pyramid, multiplying this number by the ratio of its length to the size 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. Furthermore, Tales is the person who is considered the initial 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 some time, went along to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken up to Babylon by capturing the Persians through the occupation of Egypt by the Persians. it’s 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 instruct 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 individuals of this school called “mathematics” live together and they are connected to one another with oath. The 2nd group includes students attending school. Pythagoras school is founded on number cult. According to them, everything can be reduced to numbers; It has an unusually perfect harmony among numbers, and harmony is just 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 called the Pythagorean theorem (the square of the right sides of a right triangle equals the square of the hypotenuse) put the Pythagorean school in a deep crisis. The discovery of irrational numbers is the very first major crisis of mathematics. Many of the members of the Pythagorean school were massacred with 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 quite some time under this or that name. As may be understood from these details, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.

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