Math in Focus Chapter 3: Bar Modeling for Word Problems | Math

Math in Focus Chapter 3: Bar Modeling for Word Problems

Shut the Door and Teach: Math in Focus Chapter 3: Bar Modeling for Word Problems

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 with time; it is no further possible to describe it in a few sentences. What I have to state now is going to be words that emphasize its various aspects, rather than 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 truth that a work done, a developed theory works in one of the ways or another apart from mathematics does not concern them much. What matters in their mind could be the depth of the task done, the novelty of the methods used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is just a language. If the goal of science is the universe; If it’s to comprehend, rule and direct everything in the universe, we ought to be able 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 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 only a tool for its user. After entering it, we understand and perceive what mathematics is inside our 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 those that deal 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 word mathematics, for initially, BC. It had been employed by the members of the Pythagorean school in the 550s. His entry in to the written literature, with Plato BC. It had been in the 380s. The word meaning is “what must be learned”, that is, information. In the years before these dates, rather than the word mathematics, words that mean geometry, comparable to it in geometry or old languages ​​were used.

It’s difficult to state anything definite about where and how mathematics started. If we take documents that are not based on archaeological findings that need interpretation, but open enough to require interpretation, We could say so it started between 3000 and 2000 in Egypt and Mesopotamia. Based on Heredotus (485-415 BC), mathematics were only available in Egypt. Everbody knows, 97% of the Egyptian lands aren’t suitable for agriculture; It is the 3% portion that gives life to Egypt and forms the Nile delta. Therefore, these lands are extremely valuable. However, by the end of the floods due to the Nile river annually, the boundaries of the landowners’lands become obscure. Considering that 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 arrive at take the mandatory measurements and supply the landowners the maximum amount of land as they’d in the earlier year. Herodotus says that geometry has begun to emerge as a result of those measurements and calculations. Another opinion in regards to the birth of mathematics is usually the one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics was born in Egypt. But it was created out from the boredom of clergymen and priests, not the need for measurement-calculation caused by Nile floods. At that time, the sole intellectual class of countries such as for instance Egypt was the priest class. Considering that the livelihood of the class is supplied by the general public or the state, they’ve much time for you to share with intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of that point, just like others invented games like chess, bridge, and go&hellip ;.Both these views might be true; priests wished to simplify the work of the geometric, or they discovered how exactly to calculate the aspects of some geometric shapes such as triangular and trapezoidal to test that the distribution was fair, and this way generated the birth of geometry.

We shall divide the written history of mathematics into five periods. The first period will 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 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, referred to as the golden age of mathematics, dating from 1700-1900. The time we are residing in, dating back again to the 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 spot of mathematics in social life and the fundamental top features of mathematics in that 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. You can find two major causes for this. The very first is that the ancient Egyptians wrote the writing on papyrus; The next reason may be the 3 big fires of the Alexandria libraries, the final of the fires happened throughout 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 word papyrus. The common lifespan of a papyrus is 300 years; 300 years later, it is flaky due to moisture, heat and similar reasons. To date, two papyrus related to mathematics appear to possess been hidden under exceptional circumstances. The main resources of our familiarity with Egyptian mathematics are those two papyri. The initial of those papyrus is just 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 really 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 book written to instruct math. In the introduction part, following a few exercises given to show operations with fractional numbers, 87 questions are shown using their solutions. These are the type of questions people can encounter in lifestyle, such as sharing account, interest calculation, or finding the location of ​​some geometric shapes. This really is pretty much our 8th grade mathematics. The 2nd papyrus, known 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 type of questions in the Ahmes papyrus, with the exception of the two. As for the other two questions, one of them may be the calculation of the amount and section of ​​the surface of the sphere part cut with a plane. One other is the question of finding the amount of a pyramid cut by way of a plane. Both questions were solved correctly. Both of these questions are accepted while the pinnacle of Egyptian mathematics. The Egyptians realized that the location 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 at this level for 2000 years and hasn’t made any significant progress.

B.C. 600s are 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, 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 beginning 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 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. During Egypt, it’s described in books where he calculates the height of the fantastic pyramid by measuring the length of the shadow of the truly amazing 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 a group around him to teach what he learned. It is assumed that abstract proof based on reasoning, which is not centered on mathematics – experimental verification, entered into Tales. Additionally, Tales is the person who is known as the very 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 a while, visited 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 returning to Samos, he created a college and tried to instruct individuals 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 individuals of this school called “mathematics” live together and they are connected together with oath. The 2nd group includes students attending school. Pythagoras school is based on number cult. According to them, everything may 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 example 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 a right triangle equals the square of the hypotenuse) put the Pythagorean school in a deep crisis. The discovery of irrational numbers is the first major crisis of mathematics. Most of the members of the Pythagorean school were massacred by a raid led by 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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