Systems of Inequalities ~ Matching Systems and Graphs Activity | Math

Systems of Inequalities ~ Matching Systems and Graphs Activity

This Systems of Linear Inequalities activity requires students to match systems of linear inequalities to their solution set graphs.This activity includes 16 systems of inequalities and 20 graphs (4 of which are extras to prevent student guessing). Stude

MATHEMATIC HISTORY

Mathematics is one of 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 as time passes; it is no longer possible to describe it in several sentences. What I have to state now is going to be words that emphasize its various aspects, rather than describe mathematics. In one aspect, mathematics is an art form like painting and music. A large proportion of mathematicians perform it being an art. Using this perspective, 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 to them could be the depth of the job done, the novelty of the strategy used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is a language. If the objective of science is the universe; If it’s to understand, rule and direct everything in the universe, we should 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 need to know the language of mathematics. In another aspect, mathematics can be an intellectual game like chess.

Some mathematicians also notice it as a game. Mathematics is just a tool for the user. After entering it, we understand and perceive what mathematics is inside our knowledge and in the direction of our interest. Mathematics has become far beyond the dimensions any human can rule. Therefore, I don’t believe that those who deal with mathematics are more than we understand and perceive it from mathematics than the blind touched net understands and perceives the elephant. The term mathematics, for initially, BC. It was used by the members of the Pythagorean school in the 550s. His entry into the written literature, with Plato BC. It was in the 380s. The term meaning is “what needs to be learned”, that’s, information. In the years before these dates, rather than the word mathematics, words which means that geometry, equivalent to it in geometry or old languages ​​were used.

It is not possible to state anything definite about where and how mathematics started. If we take documents that aren’t predicated on archaeological findings that require interpretation, but open enough to require interpretation, We can 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 suited to agriculture; It is the 3% portion that provides 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 and every flood, the “geometricists” of their state, who’re responsible for these works, should arrived at take the necessary 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 as a result of the measurements and calculations. An additional opinion in regards to 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 requirement for measurement-calculation caused by Nile floods. During those times, the only intellectual class of countries such as for example Egypt was the priest class. Considering that the livelihood with this class is supplied by people or their state, they have much time for you to give intellectual pursuits. To keep them busy, they invented geometry and arithmetic, the mathematics of that time, just as others invented games like chess, bridge, and go&hellip ;.Both these views might be true; priests wanted to simplify the work of the geometric, or they discovered how to calculate the areas 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 will divide the written history of mathematics into five periods. The initial period will be Egypt and Mesopotamia; this period BC In 2000s BC. It will cover an amount of 1500-2000 years between 500s. The 2nd period, BC. 500-M.S. It will cover a period of 1000 years, known 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, referred to as the golden age of mathematics, dating from 1700-1900. The period we are living in, dating back again to the early 1900s, called the age of modern mathematics, will be the fifth period. I will try to give details about the development of mathematics for the reason that period, contributing mathematicians, the area of mathematics in social life and the basic features of mathematics for the reason 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 will find two significant reasons for this. The first is that the ancient Egyptians wrote the writing on papyrus; The second reason is the 3 big fires of the Alexandria libraries, the past of the 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, on average 15-25 meters long and 30-50 inches wide. These leaves were used to create text in place of paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are produced from the phrase papyrus. The typical lifespan of a papyrus is 300 years; 300 years later, it’s flaky as a result of moisture, heat and similar reasons. Currently, two papyrus linked to mathematics appear to have been hidden under exceptional circumstances. The main sources of our knowledge of Egyptian mathematics are both of these papyri. The initial of the papyrus is just 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 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 teach math. In the introduction part, after having a few exercises given to instruct operations with fractional numbers, 87 questions are shown with their solutions. These are the kind of questions people can encounter in lifestyle, such as for example sharing account, interest calculation, or finding the area of ​​some geometric shapes. This is more or less our 8th grade mathematics. The 2nd 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, with the exception of the two. Are you aware that other two questions, one could be the calculation of the amount and part of ​​the surface of the sphere part cut by a plane. One other is the question of finding the amount of a pyramid cut by way of a plane. Both questions were solved correctly. These two questions are accepted because the pinnacle of Egyptian mathematics. The Egyptians seen that the region of ​​the circle was proportional to its diameter and found how many 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 has not made any significant progress.

B.C. 600s are the years when 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, annually later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 is the date that was accepted as the start 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. Two people, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as being the father of Greek mathematics. Tales Milet (Aydın) was also born. It is known he visited Egypt, stayed there for a time and learned geometry in Egypt. Whilst in Egypt, it’s described in books where he calculates the height of the truly amazing pyramid by measuring the size of the shadow of the fantastic pyramid, multiplying this number by the ratio of its length to along the existing shadow. After returning to Tales Milet, he taught them geometry by forming friends around him to teach what he learned. It is assumed that abstract proof predicated on reasoning, which is not based on mathematics – experimental verification, entered into Tales. Additionally, Tales is the person who is known as 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 a while, went along to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken up 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 teach 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 individuals of this school called “mathematics” live together and they’re connected together with oath. The 2nd group contains students attending school. Pythagoras school is based on number cult. According in their mind, everything may 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 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 referred to 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 deep crisis. The discovery of irrational numbers is the very 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 few years he died. Pythagoras’thoughts, the Pythagorean school lived for quite some time under this or that name. As can be understood from these records, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.

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