3rd Grade Math: Multiplication and Division Part 2
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 is no more possible to spell it out it in a couple of sentences. What I’ve to say now will undoubtedly be words that emphasize its various aspects, rather than describe mathematics. In one aspect, mathematics is an art like painting and music. The vast majority of mathematicians perform it as an art. From this viewpoint, the fact a work done, a developed theory works in one way or another apart from mathematics doesn’t concern them much. What matters for them may be 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 just a language. If the goal of science could be the universe; If it’s to know, 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 have to know the language of mathematics. In another aspect, mathematics is definitely an intellectual game like chess.
Some mathematicians also notice 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 has become far beyond the dimensions any human can rule. Therefore, I do not genuinely believe that those who handle mathematics are far 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 had been used by the members of the Pythagorean school in the 550s. His entry into the written literature, with Plato BC. It had been in the 380s. The word meaning is “what needs to be learned”, that’s, information. In the years before these dates, as opposed to the word mathematics, words that mean geometry, comparable 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 centered on archaeological findings that require interpretation, but open enough to require interpretation, We could say so it started between 3000 and 2000 in Egypt and Mesopotamia. In accordance with Heredotus (485-415 BC), mathematics were only available in Egypt. Everbody knows, 97% of the Egyptian lands are not ideal 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 every year, the boundaries of the landowners’lands become obscure. Because the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of the state, who’re accountable for these works, should arrive at take the required measurements and provide the landowners the maximum amount of land as they’d in the last year. Herodotus says that geometry has begun to emerge consequently of the measurements and calculations. A second opinion in regards to the birth of mathematics is the main one put forward by Aristotle (384-322 BC). Based on Aristotle, mathematics was born in Egypt. But it came to be out from the boredom of clergymen and priests, not the requirement for measurement-calculation due to Nile floods. During those times, the sole intellectual class of countries such as Egypt was the priest class. Considering that the livelihood with this class is given by the public or the state, they’ve much time 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 may be true; priests wanted to simplify the task of the geometric, or they found out how to calculate the regions of some geometric shapes such as triangular and trapezoidal to check that the distribution was fair, and in this manner resulted in the birth of geometry.
We shall 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 second period, BC. 500-M.S. It’ll cover a period of 1000 years, called 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 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, known as the golden age of mathematics, dating from 1700-1900. The time scale we are residing in, dating back again to the first 1900s, called age modern mathematics, would be the fifth period. I will attempt to give information regarding the development of mathematics because period, contributing mathematicians, the area of mathematics in social life and the fundamental features of mathematics for the reason that period.
We will start the very 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 first is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason could be the 3 big fires of the Alexandria libraries, the past of the fires happened throughout 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, normally 15-25 meters long and 30-50 inches wide. These leaves were used to write text as opposed to paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages such as “Paper”, “papier” are based on the phrase papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it is flaky as a result of moisture, heat and similar reasons. Up to now, two papyrus linked to mathematics appear to have been hidden under exceptional circumstances. The key sources of our knowledge of Egyptian mathematics are these two papyri. The very first of these papyrus is really 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 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 guide written to teach math. In the introduction part, after a few exercises given to teach operations with fractional numbers, 87 questions get making use of their solutions. They are the type of questions people can encounter in daily life, such as sharing account, interest calculation, or finding the region of some geometric shapes. This is more or less our 8th grade mathematics. The second papyrus, called the Moscow papyrus and now in the Moscow museum, can also be BC. It is 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. Are you aware that other two questions, one 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 volume of a pyramid cut by a plane. Both questions were solved correctly. These two questions are accepted as the pinnacle of Egyptian mathematics. The Egyptians realized that the region 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’s understood that Egyptian mathematics has remained at this level for 2000 years and hasn’t made any significant progress.
B.C. 600s would be the years once the Persians started to dominate the center east. B.C. By the 550s, Persians are the only real rulers of the whole 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 could be the date that has been 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 prior to when 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 famous he went to Egypt, stayed there for a time and learned geometry in Egypt. During Egypt, it’s described in books where he calculates the height of the great pyramid by measuring the size of the shadow of the great pyramid, multiplying this number by the ratio of its length to the size of the existing shadow. After returning to Tales Milet, he taught them geometry by forming an organization around him to teach what he learned. It’s assumed that abstract proof predicated on reasoning, which can be not based on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the one who is considered the initial 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 during 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 show 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 together with oath. The next group includes students attending school. Pythagoras school is dependant on number cult. According for them, everything may 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,… 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 right 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. 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 several years under this or that name. As may be understood from this information, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.