Year 6 SATs Maths Revision – KS2 | Maths Boot Camp
Mathematics is one of 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 with time; it’s no longer possible to spell it out it in a couple of sentences. What I’ve to express now will be words that emphasize its various aspects, rather than describe mathematics. In one aspect, mathematics is an art form like painting and music. The vast majority of mathematicians perform it being an art. From this point of view, the fact that 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 could be the depth of the work done, the novelty of the strategy used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really a language. If the purpose of science could be the universe; If it is to know, rule and direct everything in the universe, we must have the ability 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 see it as a game. Mathematics is just 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 don’t believe that people who handle mathematics are more than we understand and perceive it from mathematics compared to 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’s, information. In the years before these dates, instead of the word mathematics, words that mean geometry, equal to it in geometry or old languages were used.
It is difficult to say anything definite about where and how mathematics started. When we take documents which are not centered on archaeological findings that want interpretation, but open enough to require interpretation, We can 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 are not suitable for agriculture; It’s the 3% portion that provides life to Egypt and forms the Nile delta. Therefore, these lands are incredibly valuable. However, at the conclusion of the floods due to 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 flood, the “geometricists” of their state, that are in charge of these works, should arrived at take the mandatory measurements and provide the landowners just as much land as they had in the earlier year. Herodotus says that geometry has begun to emerge as a result of the measurements and calculations. Another opinion about the birth of mathematics is the one put forward by Aristotle (384-322 BC). In accordance with Aristotle, mathematics was born in Egypt. Nonetheless it came to be out from the boredom of clergymen and priests, not the need for measurement-calculation caused by Nile floods. During those times, the only intellectual class of countries such as Egypt was the priest class. Because the livelihood of the class is given by people or their state, they’ve much time and energy to give intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of the period, in the same way others invented games like chess, bridge, and go&hellip ;.Both these views might be true; priests desired to simplify the task of the geometric, or they discovered how exactly to calculate the aspects of some geometric shapes such as for instance triangular and trapezoidal to test that the distribution was fair, and in this manner resulted in the birth of geometry.
We will divide the written history of mathematics into five periods. The first period will 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 will cover a period of 1000 years, referred to 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 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 surviving in, dating back to the early 1900s, called the age of modern mathematics, would be the fifth period. I will attempt to give details about the development of mathematics because period, contributing mathematicians, the place of mathematics in social life and the fundamental 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 main reasons for this. The very first is that the ancient Egyptians wrote the writing on papyrus; The second reason may be the 3 big fires of the Alexandria libraries, the last of those fires happened during 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, on average 15-25 meters long and 30-50 inches wide. These leaves were used to publish 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 common lifespan of a papyrus is 300 years; 300 years later, it is flaky due to moisture, heat and similar reasons. Up to now, two papyrus linked to mathematics appear to have been hidden under exceptional circumstances. The key sourced elements of our familiarity with Egyptian mathematics are both of these papyri. The very first of the 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 compiled 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 teach math. In the introduction part, after having a few exercises given to instruct operations with fractional numbers, 87 questions are made making use of their solutions. These are the type of questions people can encounter in everyday life, such as for example sharing account, interest calculation, or finding the location of some geometric shapes. This is just about our 8th grade mathematics. The second papyrus, referred to 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 kind of questions in the Ahmes papyrus, except for the two. As for the other two questions, one of them may be the calculation of the amount and part of the surface of the sphere part cut by way of a plane. The other could be the question of finding the amount of a pyramid cut with 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 amount 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 hasn’t made any significant progress.
B.C. 600s will be the years once the Persians started to dominate the center east. B.C. By the 550s, Persians are the sole 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, a year 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 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 daddy of Greek mathematics. Tales Milet (Aydın) was also born. It is famous he went along to Egypt, stayed there for some time 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 truly amazing pyramid, multiplying this number by the ratio of its length to the length of the current shadow. After time for Tales Milet, he taught them geometry by forming friends around him to teach what he learned. It’s assumed that abstract proof centered on reasoning, which is not based on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the person who is known 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 while, went along to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken to Babylon by capturing the Persians through 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 college and tried to instruct 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 people of this school called “mathematics” live together and they are connected to each other with oath. The next group consists of students attending school. Pythagoras school is dependant on number cult. According for them, everything could be reduced to numbers; It posseses 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 example 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 known as 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 first major crisis of mathematics. Many of the members of the Pythagorean school were massacred by way of a raid led with a big cyber named Cylon. Pythagoras saved his life, but after a few 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 cornerstone of Greek mathematics.