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 one of the oldest sciences in human history. In ancient times, Mathematics was defined since the science of numbers and shapes. Mathematics, like other branches of science, has evolved over time; it’s no further possible to describe it in a few sentences. What I’ve to say now is going to 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 great majority of mathematicians perform it being an art. Using this viewpoint, the truth that a work done, a developed theory works in one way or another other than mathematics does not 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 a language. If the purpose of science is the universe; If it’s to comprehend, rule and direct everything in the universe, we ought to have the ability to read 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 have 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 within our knowledge and in the direction of our interest. Mathematics is now far beyond the dimensions any human can rule. Therefore, I don’t believe people who 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 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 word meaning is “what must be learned”, that’s, information. In the years before these dates, rather than the word mathematics, words that mean geometry, equal to it in geometry or old languages ​​were used.

It is extremely hard 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 so it started between 3000 and 2000 in Egypt and Mesopotamia. Based on Heredotus (485-415 BC), mathematics were only available in Egypt. As you know, 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 incredibly valuable. However, at the conclusion of the floods due to the Nile river every year, the boundaries of the landowners’lands become obscure. Considering that the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of the state, who are accountable for these works, should arrive at take the required measurements and provide the landowners as much land as they had in the earlier year. Herodotus says that geometry has begun to emerge consequently of these measurements and calculations. Another opinion concerning the birth of mathematics is the main one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics came to be in Egypt. But it was born from the boredom of clergymen and priests, not the requirement for measurement-calculation due to Nile floods. During those times, the only intellectual class of countries such as Egypt was the priest class. Because the livelihood of this class is provided by the general public or the state, they’ve much time and energy to share with intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of the period, in the same way others invented games like chess, bridge, and go&hellip ;.These two views may be true; priests wished to simplify the task of the geometric, or they discovered how exactly to calculate the regions of some geometric shapes such as for instance triangular and trapezoidal to test that the distribution was fair, and in this way led to the birth of geometry.

We will divide the written history of mathematics into five periods. The 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 next 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 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 are residing in, dating back to early 1900s, called the age of modern mathematics, will be the fifth period. I will try to offer information regarding the development of mathematics because period, contributing mathematicians, the place of mathematics in social life and the essential features of mathematics in that period.

We shall start the initial 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 major causes for this. The 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 final of these fires happened during 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 instead 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 is flaky due to moisture, heat and similar reasons. To date, two papyrus linked to mathematics appear to have been hidden under exceptional circumstances. The key resources of our knowledge of Egyptian mathematics are both of these papyri. The first of these papyrus is 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 really 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 show math. In the introduction part, following a few exercises given to teach operations with fractional numbers, 87 questions get with their solutions. They’re the type of questions people can encounter in daily life, such as for instance sharing account, interest calculation, or finding the area of ​​some geometric shapes. This really is pretty much 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 sort of questions in the Ahmes papyrus, aside from the two. Are you aware that other two questions, one may be the calculation of the quantity and area of ​​the surface of the sphere part cut by way of a plane. Another is the question of finding the amount of a pyramid cut with a plane. Both questions were solved correctly. Those two questions are accepted whilst the pinnacle of Egyptian mathematics. The Egyptians realized that the region 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 at this level for 2000 years and hasn’t made any significant progress.

B.C. 600s would be the years once the Persians began to dominate the middle east. B.C. By the 550s, Persians are the sole 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, a year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 is the date that was accepted as the beginning 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. A couple, 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 famous that he went to 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 fantastic pyramid by measuring the length 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 instruct what he learned. It is assumed that abstract proof predicated on reasoning, which will be not centered on mathematics – experimental verification, entered into Tales. In addition, Tales is the one who is known 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 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 is 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 instruct individuals 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 folks of this school called “mathematics” live together and they are connected to each other with oath. The next group contains students attending school. Pythagoras school is founded on number cult. According for them, everything may be reduced to numbers; It posseses 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 instance 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 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 heavy crisis. The discovery of irrational numbers is the first major crisis of mathematics. Most 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 a few years he died. Pythagoras’thoughts, the Pythagorean school lived for many years under this or that name. As may be understood from these details, Egyptian and Mesopotamian mathematics are the basis of Greek mathematics.