Number sense & numeration: grade 8 dividing fractions – Google Search
Mathematics is among the oldest sciences in human history. In ancient times, Mathematics was defined because the science of numbers and shapes. Mathematics, like other branches of science, has evolved over time; it is no more possible to describe it in several sentences. What I’ve to say now is likely to be words that emphasize its various aspects, rather than describe mathematics. In one aspect, mathematics is an art form 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 of the ways or another besides mathematics does not concern them much. What matters in their mind is the depth of the job 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 objective of science is the universe; If it is to know, rule and direct everything in the universe, we ought to be able 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 need to know the language of mathematics. In another aspect, mathematics is an intellectual game like chess.
Some mathematicians also see it as a game. Mathematics is only a tool for the 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 don’t believe 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 absolutely was employed by the members of the Pythagorean school in the 550s. His entry into 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, equal to it in geometry or old languages were used.
It’s not possible to say anything definite about where and how mathematics started. When we take documents that aren’t based on archaeological findings that want interpretation, but open enough to require interpretation, We could 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 ideal for agriculture; It is the 3% portion that gives life to Egypt and forms the Nile delta. Therefore, these lands are incredibly valuable. However, by the end of the floods brought on 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 flood, the “geometricists” of their state, that are accountable for these works, should arrive at take the necessary measurements and supply the landowners just as much land as they had in the previous year. Herodotus says that geometry has begun to emerge consequently of the measurements and calculations. An additional opinion about the birth of mathematics is the main one put forward by Aristotle (384-322 BC). In accordance with Aristotle, mathematics was born in Egypt. But it came to be from the boredom of clergymen and priests, not the need for measurement-calculation due to Nile floods. At that time, 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 have much time and energy to give to intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of that point, in the same way 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 found out how to calculate the areas of some geometric shapes such as for instance triangular and trapezoidal to test that the distribution was fair, and in this way resulted in the birth of geometry.
We will 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’ll cover a period of 1500-2000 years between 500s. The 2nd period, BC. 500-M.S. It’ll cover an amount 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, known as the golden age of mathematics, dating from 1700-1900. The time we are residing in, dating back to the first 1900s, called the age of modern mathematics, would be the fifth period. I will attempt to provide details about the development of mathematics for the reason that period, contributing mathematicians, the place of mathematics in social life and the basic options that come with mathematics because period.
We will start the initial 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 first is that the ancient Egyptians wrote the writing on papyrus; The second reason is the 3 big fires of the Alexandria libraries, the past of these fires happened through 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, an average of 15-25 meters long and 30-50 inches wide. These leaves were used to publish text in place of 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 average lifespan of a papyrus is 300 years; 300 years later, it’s flaky due to moisture, heat and similar reasons. To date, two papyrus related to mathematics appear to own been hidden under exceptional circumstances. The key resources of our knowledge of Egyptian mathematics are both of these 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’re a puree written in 2000s, BC. It is 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 show math. In the introduction part, following a few exercises given to instruct operations with fractional numbers, 87 questions are made making use of their solutions. They’re the type of questions people can encounter in daily life, such as sharing account, interest calculation, or finding the location of some geometric shapes. This is pretty much our 8th grade mathematics. The 2nd papyrus, referred to 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 sort of questions in the Ahmes papyrus, aside from the two. As for the other two questions, one of them may be the calculation of the volume and part of the surface of the sphere part cut by a plane. Another is the question of finding the quantity of a pyramid cut by way of a plane. Both questions were solved correctly. These two questions are accepted since the pinnacle of Egyptian mathematics. The Egyptians seen 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 only at that level for 2000 years and has not made any significant progress.
B.C. 600s would be the years when the Persians started to dominate the center east. B.C. By the 550s, Persians are the only 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 may be the date that has been accepted as the start 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. A couple, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as the daddy of Greek mathematics. Tales Milet (Aydın) was also born. It is famous he went to Egypt, stayed there for a while and learned geometry in Egypt. While in Egypt, it is described in books where he calculates the height of the fantastic pyramid by measuring along the shadow of the fantastic pyramid, multiplying this number by the ratio of its length to along the present 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 centered on reasoning, which will be not centered on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the person who is recognized as 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, 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 throughout 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 teach the people 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 next group includes students attending school. Pythagoras school is founded on number cult. According in their mind, everything could be reduced to numbers; It has 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 instance 1,2,3,…; and kes, ¾,… will be 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 proper 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 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 quite some time under this or that name. As could be understood from this information, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.