Maths study notes for GCSE revision! I’ve seen a lot of study notes on Instagram and I love how they look so I’ve decided that I’m going to…
Mathematics is one of many 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’s no longer possible to explain it in a few sentences. What I’ve to say now will undoubtedly be words that emphasize its various aspects, as opposed to describe mathematics. In taking care of, mathematics is a skill like painting and music. The great majority of mathematicians perform it as an art. Using this standpoint, the fact a work done, a developed theory works in one of the ways or another other than mathematics doesn’t 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 purpose of science could be the universe; When it is to know, rule and direct everything in the universe, we ought to manage to read 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 definitely 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 in your knowledge and in the direction of our interest. Mathematics is now far beyond the dimensions any human can rule. Therefore, I do not believe that those who deal with mathematics tend to be more than we understand and perceive it from mathematics compared to blind touched net understands and perceives the elephant. The term mathematics, for the very first time, BC. It absolutely was 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 is, information. In the years before these dates, rather than the word mathematics, words that mean geometry, equivalent to it in geometry or old languages were used.
It’s not possible to express anything definite about where and how mathematics started. When we take documents that are not based on archaeological findings that need interpretation, but open enough to require interpretation, We could 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 suited to agriculture; It is the 3% portion that gives life to Egypt and forms the Nile delta. Therefore, these lands are extremely valuable. However, at the end 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, who’re responsible for these works, should arrive at take the necessary measurements and give the landowners just as much land as they’d in the previous year. Herodotus says that geometry has begun to emerge consequently of these measurements and calculations. A second opinion about the birth of mathematics is the one put forward by Aristotle (384-322 BC). In accordance with Aristotle, mathematics came to be in Egypt. However it came to be out of the boredom of clergymen and priests, not the requirement for measurement-calculation caused by Nile floods. At that time, the sole intellectual class of countries such as Egypt was the priest class. Because the livelihood of this class is supplied by the public or their state, they’ve much time to give intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of that point, just as others invented games like chess, bridge, and go&hellip ;.Both these views may be true; priests wanted to simplify the task of the geometric, or they learned how 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 way led to the birth of geometry.
We will divide the written history of mathematics into five periods. The first period is likely to be Egypt and Mesopotamia; this period BC In 2000s BC. It will cover an amount of 1500-2000 years between 500s. The next period, BC. 500-M.S. It will cover a period 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 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 period we are living in, dating back once again to the first 1900s, called the age of modern mathematics, could be the fifth period. I will attempt to offer information about the development of mathematics because period, contributing mathematicians, the place of mathematics in social life and the fundamental features of 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. You can find two major causes for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The next reason is the 3 big fires of the Alexandria libraries, the past of the 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, typically 15-25 meters long and 30-50 inches wide. These leaves were used to write text instead 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 common 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 possess been hidden under exceptional circumstances. The key resources of our familiarity with Egyptian mathematics are these two papyri. The first of these papyrus is really a 6-meter long and 35-cm wide papyrus known as the Ahmes (or Rhind) papyrus. This papyrus, BC. You are 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 teach math. In the introduction part, after having a few exercises given to instruct operations with fractional numbers, 87 questions get making use of their solutions. They’re the sort of questions people can encounter in everyday life, such as for instance sharing account, interest calculation, or finding the region of some geometric shapes. This really is more or less our 8th grade mathematics. The next papyrus, referred to as the Moscow papyrus and now in the Moscow museum, can also be BC. It is really a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the kind of questions in the Ahmes papyrus, aside from the two. When it comes to other two questions, one may be the calculation of the volume and area of the surface of the sphere part cut by a plane. Another is the question of finding the volume of a pyramid cut by way of a plane. Both questions were solved correctly. These two 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 the amount 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 has not made any significant progress.
B.C. 600s would be the years once the Persians started initially 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, a year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 could be the date which was accepted as the beginning of Greek civilization. This date is the start of a really bright period in science, art and literature. Greek mathematics actually started sooner than this period. A couple, 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 he visited 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 truly amazing pyramid by measuring along the shadow of the fantastic pyramid, multiplying this number by the ratio of its length to the length of the existing shadow. After time for Tales Milet, he taught them geometry by forming friends around him to show what he learned. It’s assumed that abstract proof based on reasoning, which will be not predicated 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 time, 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 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 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 folks of this school called “mathematics” live together and they’re connected to one another with oath. The next group contains students attending school. Pythagoras school is founded on number cult. According to them, everything could 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 for instance 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 the right triangle equals the square of the hypotenuse) put the Pythagorean school in a strong crisis. The discovery of irrational numbers is the initial major crisis of mathematics. Most 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 many years he died. Pythagoras’thoughts, the Pythagorean school lived for quite some time under this or that name. As can be understood from these details, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.