The Math Formulas You Should Memorize For The SAT | Math

The Math Formulas You Should Memorize For The SAT

The Math Formulas You Should Memorize For The SAT

MATHEMATIC HISTORY

Mathematics is among the oldest sciences in human history. In ancient times, Mathematics was defined as the science of numbers and shapes. Mathematics, like other branches of science, has evolved as time passes; it is no longer possible to spell it out it in several sentences. What I’ve to express now is going to be words that emphasize its various aspects, as opposed to describe mathematics. In one aspect, mathematics is an art like painting and music. The vast majority of mathematicians perform it as an art. Using this point of view, the fact a work done, a developed theory works in one way or another other than mathematics does not concern them much. What matters to them 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 a language. If the purpose of science could be the universe; When it is to understand, rule and direct everything in the universe, we must have the ability 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 because of its 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 think that those that deal with mathematics tend to be 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 very first time, BC. It 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’s, information. In the years before these dates, instead of the word mathematics, words which means that geometry, equal to it in geometry or old languages ​​were used.

It is not possible to say anything definite about where and how mathematics started. When we take documents that are not predicated on archaeological findings that require interpretation, but open enough to require interpretation, We could say that it started between 3000 and 2000 in Egypt and Mesopotamia. Based on Heredotus (485-415 BC), mathematics started in Egypt. As you 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, by the end of the floods caused by the Nile river annually, the boundaries of the landowners’lands become obscure. Because the landowners also pay taxes in proportion to the land they own, after each flood, the “geometricists” of the state, who are in charge of these works, should arrive at take the necessary measurements and give the landowners as much land as they’d in the previous year. Herodotus says that geometry has begun to emerge as a result of the measurements and calculations. Another opinion concerning the birth of mathematics is usually the one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics was born 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. At that time, the sole intellectual class of countries such as for instance Egypt was the priest class. Considering that the livelihood of this class is given by people or the state, they’ve much time for you to share with intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of that time, just like others invented games like chess, bridge, and go&hellip ;.Both of these views may be true; priests desired to simplify the task of the geometric, or they learned how to calculate the areas of some geometric shapes such as triangular and trapezoidal to check on that the distribution was fair, and this way resulted in the birth of geometry.

We shall divide the written history of mathematics into five periods. The very first period will soon be Egypt and Mesopotamia; this period BC In 2000s BC. It’ll cover a period of 1500-2000 years between 500s. The second 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’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, known as the golden age of mathematics, dating from 1700-1900. The period we’re living in, dating back once again to the first 1900s, called age modern mathematics, would be the fifth period. I will attempt to offer information regarding the development of mathematics because period, contributing mathematicians, the area of mathematics in social life and the essential options that come with 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 significant reasons for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason could be the 3 big fires of the Alexandria libraries, the past of those fires happened during the conquest of Egypt by 641 Muslims, the written documents disappeared. Papyrus is 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 derived from the term 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 related to mathematics appear to own been hidden under exceptional circumstances. The key sources of our knowledge of Egyptian mathematics are those 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 really 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, following a few exercises given to show operations with fractional numbers, 87 questions receive making use of their solutions. They are the type of questions people can encounter in daily life, such as for example sharing account, interest calculation, or finding the area of ​​some geometric shapes. This really is more or less our 8th grade mathematics. The next papyrus, called 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. When it comes to other two questions, one of them may be the calculation of the amount and section of ​​the surface of the sphere part cut by way of a plane. The other may be the question of finding the amount of a pyramid cut with a plane. Both questions were solved correctly. These two questions are accepted as 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 is understood that Egyptian mathematics has remained as of this 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 real 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 has been accepted as the start of Greek civilization. This date is the beginning of a really bright period in science, art and literature. Greek mathematics actually started sooner than 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 known he visited Egypt, stayed there for a while and learned geometry in Egypt. During Egypt, it is described in books where he calculates the height of the truly amazing pyramid by measuring along the shadow of the great pyramid, multiplying this number by the ratio of its length to the size of the present shadow. After time for Tales Milet, he taught them geometry by forming an organization around him to show what he learned. It is assumed that abstract proof based on reasoning, which is not based on mathematics – experimental verification, entered into Tales. In addition, Tales is the person who is known as the first philosopher in human history. He was created on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for a while, visited Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken up 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 college 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 people of this school called “mathematics” live together and they are connected together with oath. The 2nd group includes students attending school. Pythagoras school is dependant on number cult. According for them, everything can 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 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 known as the Pythagorean theorem (the square of the proper sides of a right triangle equals the square of the hypotenuse) put the Pythagorean school in a strong crisis. The discovery of irrational numbers is the very first major crisis of mathematics. Many of the members of the Pythagorean school were massacred with 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 can be understood from this information, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.

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