Patent revision sheet: all the formulas to know in math – Collège Pierre Perret
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’s no further possible to explain it in a couple of sentences. What I have to state now will soon 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 vast majority of mathematicians perform it being an art. From this perspective, the fact a work done, a developed theory works in one way or another besides mathematics doesn’t concern them much. What matters in their mind could be the depth of the job done, the novelty of the techniques used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really a language. If the goal of science is the universe; When it is 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 have to know the language of mathematics. In another aspect, mathematics can be an intellectual game like chess.
Some mathematicians also see it as a game. Mathematics is merely a tool for its user. After entering it, we understand and perceive what mathematics is in your knowledge and in the direction of our interest. Mathematics is currently far beyond the dimensions any human can rule. Therefore, I don’t believe people who cope with mathematics are more than we understand and perceive it from mathematics than the blind touched net understands and perceives the elephant. The word mathematics, for initially, BC. It was used by the members of the Pythagorean school in the 550s. His entry in to the written literature, with Plato BC. It 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, equivalent to it in geometry or old languages were used.
It’s difficult to say anything definite about where and how mathematics started. If we take documents which are not centered 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. In accordance with Heredotus (485-415 BC), mathematics were only available in Egypt. Everbody knows, 97% of the Egyptian lands aren’t ideal for agriculture; It’s the 3% portion that gives life to Egypt and forms the Nile delta. Therefore, these lands are really valuable. However, at the conclusion of the floods due to 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 are responsible for these works, should come to take the required measurements and provide the landowners the maximum amount of land as they’d in the previous year. Herodotus says that geometry has begun to emerge consequently of these measurements and calculations. Another opinion about the birth of mathematics is the main one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics came to be in Egypt. Nonetheless it came to be out from the boredom of clergymen and priests, not the necessity for measurement-calculation brought on by Nile floods. In those days, the only real intellectual class of countries such as Egypt was the priest class. Because the livelihood of the class is supplied by people or their state, they’ve much time to give to intellectual pursuits. To help 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 wished to simplify the task of the geometric, or they found out just 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 led to the birth of geometry.
We shall divide the written history of mathematics into five periods. The very 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 2nd period, BC. 500-M.S. It will cover an amount of 1000 years, known as the Greek Mathematics period, between 500 years. The next term, M.S. It’ll 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, called the golden age of mathematics, dating from 1700-1900. The time scale we’re living in, dating back again to the early 1900s, called age modern mathematics, will be the fifth period. I will attempt to offer information about the development of mathematics in that period, contributing mathematicians, the area of mathematics in social life and the essential features of mathematics in 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. You can find two significant reasons for this. The very 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 last of these 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, an average of 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 based on the term papyrus. The typical lifespan of a papyrus is 300 years; 300 years later, it’s flaky due to moisture, heat and similar reasons. Currently, two papyrus related to mathematics appear to possess been hidden under exceptional circumstances. The main sourced elements of our understanding of Egyptian mathematics are those two papyri. The initial of those papyrus is really 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 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 instruct math. In the introduction part, after a few exercises given to instruct operations with fractional numbers, 87 questions are shown making use of their solutions. They are the sort of questions people can encounter in everyday life, such as for instance sharing account, interest calculation, or finding the area of some geometric shapes. That 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 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. Are you aware that other two questions, one could be the calculation of the quantity and part of the surface of the sphere part cut by a plane. The other could be the question of finding the amount of a pyramid cut by a plane. Both questions were solved correctly. These two questions are accepted because the pinnacle of Egyptian mathematics. The Egyptians realized that the area 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 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 middle 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 could be the date which was accepted as the start of Greek civilization. This date is the beginning of a very 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 considered to be the father of Greek mathematics. Tales Milet (Aydın) was also born. It is famous that he went along to Egypt, stayed there for a while and learned geometry in Egypt. During Egypt, it’s described in books where he calculates the height of the fantastic pyramid by measuring the size of the shadow of the fantastic 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 instruct what he learned. It’s assumed that abstract proof based on reasoning, which can be not predicated on mathematics – experimental verification, entered into Tales. In addition, Tales is the person who is considered the 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 some 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 during 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 show 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’re connected together with oath. The 2nd group includes students attending school. Pythagoras school is based on number cult. According in their mind, everything can be reduced to numbers; It comes with 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 referred to as 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 first major crisis of mathematics. Most of the members of the Pythagorean school were massacred with a raid led by way of a big cyber named Cylon. Pythagoras saved his life, but after many years he died. Pythagoras’thoughts, the Pythagorean school lived for several years under this or that name. As could be understood from this information, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.