Solving Quadratic Equations Paper Chain Activity | Math

Solving Quadratic Equations Paper Chain Activity

My Algebra students loved this Quadratic Equation activity. It was the perfect way for my students to get some practice solving quadratic equations. I will love doing Algebra activities like this instead of regular Algebra worksheets.

MATHEMATIC HISTORY

Mathematics is among the oldest sciences in human history. In ancient times, Mathematics was defined while the science of numbers and shapes. Mathematics, like other branches of science, has evolved with time; it’s no more possible to spell it out it in several sentences. What I’ve to say now is likely to be words that emphasize its various aspects, rather than describe mathematics. In taking care of, mathematics is an art form like painting and music. A large proportion of mathematicians perform it as an art. Out of this viewpoint, the fact a work done, a developed theory works in one of the ways or another besides mathematics doesn’t concern them much. What matters in their mind may be the depth of the work 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 objective of science is the universe; When it is to understand, 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 need to know the language of mathematics. In another aspect, mathematics is an intellectual game like chess.

Some mathematicians also see it as a game. Mathematics is just a tool because of its user. After entering it, we understand and perceive what mathematics is within our 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 cope with mathematics are far more than we understand and perceive it from mathematics compared to blind touched net understands and perceives the elephant. The phrase mathematics, for the first time, BC. It absolutely was used by the members of the Pythagorean school in the 550s. His entry 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, instead of the word mathematics, words which means that geometry, comparable to it in geometry or old languages ​​were used.

It is not possible to state anything definite about where and how mathematics started. When we take documents that are not predicated on archaeological findings that need interpretation, but open enough to require interpretation, We can say that it started between 3000 and 2000 in Egypt and Mesopotamia. Based on Heredotus (485-415 BC), mathematics were only available in Egypt. Everbody knows, 97% of the Egyptian lands aren’t 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 conclusion of the floods caused by 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 flood, the “geometricists” of their state, who’re accountable for these works, should arrive at take the necessary measurements and give the landowners just as much land as they’d in the last 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 the one put forward by Aristotle (384-322 BC). Based on Aristotle, mathematics was born in Egypt. However it came to be 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 of this class is provided by the public or the state, they’ve much time and energy 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 might be true; priests wanted to simplify the job of the geometric, or they found out just how to calculate the areas of some geometric shapes such as for instance triangular and trapezoidal to test that the distribution was fair, and in this way resulted in the birth of geometry.

We shall divide the written history of mathematics into five periods. The first period will soon be Egypt and Mesopotamia; this period BC In 2000s BC. It’ll cover an amount of 1500-2000 years between 500s. The second period, BC. 500-M.S. It will cover a period of 1000 years, known as the Greek Mathematics period, between 500 years. The next term, M.S. It will 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 period we’re residing in, dating back to the first 1900s, called age modern mathematics, would be the fifth period. I will attempt to give details about the development of mathematics for the reason that period, contributing mathematicians, the place of mathematics in social life and the fundamental top features of mathematics for the reason that period.

We will 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. There are 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 final of those fires happened throughout 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, an average of 15-25 meters long and 30-50 inches wide. These leaves were used to write text in place 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 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 own been hidden under exceptional circumstances. The main sources of our knowledge of Egyptian mathematics are those two papyri. The initial 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’re a puree written in 2000s, BC. It is really 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 book written to teach math. In the introduction part, after a few exercises given to show operations with fractional numbers, 87 questions are given using their solutions. They are the sort of questions people can encounter in daily life, such as sharing account, interest calculation, or finding the region of ​​some geometric shapes. This 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 just a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the type of questions in the Ahmes papyrus, except for the two. When it comes to other two questions, one is the calculation of the volume and area of ​​the surface of the sphere part cut by way of a plane. Another may be the question of finding the quantity of a pyramid cut by way of a plane. Both questions were solved correctly. Those two 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 how many 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 would be the years once the Persians began to dominate the center east. B.C. By the 550s, Persians are the only 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 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 earlier 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 time and learned geometry in Egypt. During Egypt, it’s described in books where he calculates the height of the great pyramid by measuring the size of the shadow of the great 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 an organization around him to show what he learned. It is assumed that abstract proof based on reasoning, which will be not predicated on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the person who is recognized as the initial philosopher in human history. He was created on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for some time, went along to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken to Babylon by capturing the Persians during 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 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 people of this school called “mathematics” live together and they’re connected to one another with oath. The second group consists of students attending school. Pythagoras school is founded on number cult. According for them, everything can be reduced to numbers; It comes with 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,… 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 right 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 initial major crisis of mathematics. Many of the members of the Pythagorean school were massacred by a raid led by a big cyber named Cylon. Pythagoras saved his life, but after many years he died. Pythagoras’thoughts, the Pythagorean school lived for many years under this or that name. As can be understood from these details, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.