High (Secondary School) Grades 11 & 12 – Math –Algebra I – … | Math

# High (Secondary School) Grades 11 & 12 – Math –Algebra I – …

High (Secondary School) Grades 11 & 12 – Math –Algebra I – …

MATHEMATIC HISTORY

Mathematics is among the oldest sciences in human history. In ancient times, Mathematics was defined whilst the science of numbers and shapes. Mathematics, like other branches of science, has evolved over time; it is no longer possible to explain it in a couple of sentences. What I have to express now is likely to be words that emphasize its various aspects, as opposed to describe mathematics. In taking care of, mathematics is an art like painting and music. The great majority of mathematicians perform it being an art. Out of this viewpoint, the fact that a work done, a developed theory works in one of the ways or another apart from mathematics doesn’t concern them much. What matters in their mind could be 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 really a language. If the goal of science could be 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. To be able 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 notice it as a game. Mathematics is merely 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 has become far beyond the dimensions any human can rule. Therefore, I do not believe people who handle mathematics are more than we understand and perceive it from mathematics compared to the blind touched net understands and perceives the elephant. The phrase mathematics, for the first time, BC. It absolutely was utilized by the members of the Pythagorean school in the 550s. His entry in to the written literature, with Plato BC. It absolutely was in the 380s. The phrase 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, comparable to it in geometry or old languages ​​were used.

It’s difficult to say anything definite about where and how mathematics started. When we take documents which are not based on archaeological findings that need interpretation, but open enough to require interpretation, We are able to say that it started between 3000 and 2000 in Egypt and Mesopotamia. According to Heredotus (485-415 BC), mathematics were only available in Egypt. You may already know, 97% of the Egyptian lands aren’t ideal for agriculture; It’s the 3% portion that offers life to Egypt and forms the Nile delta. Therefore, these lands are incredibly valuable. However, at the end of the floods due to the Nile river each year, the boundaries of the landowners’lands become obscure. Because the landowners also pay taxes in proportion to the land they own, after every flood, the “geometricists” of the state, who are responsible for these works, should arrived at take the required measurements and supply the landowners the maximum amount of land as they’d in the last year. Herodotus says that geometry has begun to emerge as a result of these measurements and calculations. Another opinion about the birth of mathematics is the one put forward by Aristotle (384-322 BC). Based on Aristotle, mathematics was born in Egypt. But it was created out from the boredom of clergymen and priests, not the necessity for measurement-calculation brought on by Nile floods. During those times, the only intellectual class of countries such as Egypt was the priest class. Considering that the livelihood of this class is given by the general public or their state, they have much time to share with intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of that point, just like others invented games like chess, bridge, and go&hellip ;.These two views may be true; priests desired to simplify the work of the geometric, or they learned just how to calculate the areas of some geometric shapes such as triangular and trapezoidal to check that the distribution was fair, and 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’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 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, called the golden age of mathematics, dating from 1700-1900. The time we’re living in, dating back once again to early 1900s, called age modern mathematics, would be the fifth period. I will endeavour to give information regarding the development of mathematics in that period, contributing mathematicians, the place of mathematics in social life and the fundamental options that come with 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 will find two major causes for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason is the 3 big fires of the Alexandria libraries, the past of those 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, an average of 15-25 meters long and 30-50 inches wide. These leaves were used to publish text rather than paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are derived from the term 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 own been hidden under exceptional circumstances. The main resources of our understanding of Egyptian mathematics are those two papyri. The very first of the 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 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 guide written to instruct math. In the introduction part, after having a few exercises given to show operations with fractional numbers, 87 questions get making use of their solutions. These are the kind of questions people can encounter in lifestyle, such as for instance sharing account, interest calculation, or finding the area of ​​some geometric shapes. This is more or less our 8th grade mathematics. The 2nd papyrus, known as the Moscow papyrus and now in the Moscow museum, can be BC. It is really 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. When it comes to other two questions, one of them could 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 amount of a pyramid cut by a plane. Both questions were solved correctly. Both of these questions are accepted whilst the pinnacle of Egyptian mathematics. The Egyptians seen 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 is understood that Egyptian mathematics has remained as of this level for 2000 years and has not made any significant progress.

B.C. 600s are the years when the Persians began to dominate the middle east. B.C. By the 550s, Persians are the only real rulers of the entire 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 was 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. Two people, 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 known he went along to Egypt, stayed there for some time and learned geometry in Egypt. While in Egypt, it’s described in books where he calculates the height of the great pyramid by measuring along the shadow of the fantastic pyramid, multiplying this number by the ratio of its length to the size of the current shadow. After returning to Tales Milet, he taught them geometry by forming an organization around him to show what he learned. It’s assumed that abstract proof centered on reasoning, which is not based on mathematics – experimental verification, entered into Tales. In addition, Tales is the one who is recognized as the very 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 a time, went along 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 show the folks 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 second group includes 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 really a reflection of the divine harmony. Known numbers for that day are integers indicating the plurality such as 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 called the Pythagorean theorem (the square of the best sides of a right triangle equals the square of the hypotenuse) put the Pythagorean school in a deep 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 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 quite some time under this or that name. As could be understood from these records, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.