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 as the science of numbers and shapes. Mathematics, like other branches of science, has evolved with time; it is no more possible to spell it out it in a few sentences. What I’ve to express now will soon be words that emphasize its various aspects, rather than describe mathematics. In one aspect, mathematics is a skill like painting and music. The great majority of mathematicians perform it being an art. Using this standpoint, the truth that a work done, a developed theory works in one way or another besides mathematics does not concern them much. What matters in their mind could be the depth of the task 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 may be 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. To be able to understand and interpret them, we must 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 only 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 is currently far beyond the dimensions any human can rule. Therefore, I don’t believe that people who handle mathematics tend to be more than we understand and perceive it from mathematics compared to blind touched net understands and perceives the elephant. The term mathematics, for the very first time, BC. It absolutely was used 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 term 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, equivalent to it in geometry or old languages ​​were used.

It’s difficult to state anything definite about where and how mathematics started. When we take documents that aren’t predicated on archaeological findings that want interpretation, but open enough to require interpretation, We are able to say that it started between 3000 and 2000 in Egypt and Mesopotamia. In accordance with Heredotus (485-415 BC), mathematics started in Egypt. As you know, 97% of the Egyptian lands aren’t suited to 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 end of the floods brought on by the Nile river each year, the boundaries of the landowners’lands become obscure. Since the landowners also pay taxes in proportion to the land they own, after every flood, the “geometricists” of their state, who are in charge of these works, should arrived at take the required measurements and supply 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. A second opinion in regards to the birth of mathematics is the one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics came to be in Egypt. But it came to be out from the boredom of clergymen and priests, not the necessity for measurement-calculation due to Nile floods. During those times, the sole intellectual class of countries such as for instance Egypt was the priest class. Since the livelihood with this class is supplied by the general public or their state, they have much time for you to give to 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 might be true; priests desired to simplify the work of the geometric, or they discovered how exactly to calculate the areas of some geometric shapes such as for example triangular and trapezoidal to check that the distribution was fair, and in this manner generated the birth of geometry.

We will divide the written history of mathematics into five periods. The very first period will be Egypt and Mesopotamia; this period BC In 2000s BC. It will 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 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 scale we are surviving in, dating back to the first 1900s, called the age of modern mathematics, will be the fifth period. I will try to give details about the development of mathematics because period, contributing mathematicians, the spot of mathematics in social life and the basic top features of 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 can find two major causes for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The 2nd reason may be 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, normally 15-25 meters long and 30-50 inches wide. These leaves were used to create text rather than paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are produced from the word papyrus. The common 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 resources of our familiarity with Egyptian mathematics are both of these papyri. The first 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 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 instruct operations with fractional numbers, 87 questions receive making use of their solutions. They’re the type of questions people can encounter in daily life, such as sharing account, interest calculation, or finding the location of ​​some geometric shapes. This really is pretty much our 8th grade mathematics. The next papyrus, called the Moscow papyrus and now in the Moscow museum, is also 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. As for the other two questions, one of them is the calculation of the volume and part of ​​the surface of the sphere part cut with a plane. The other may be the question of finding the quantity of a pyramid cut by way of a plane. Both questions were solved correctly. These two questions are accepted as the pinnacle of Egyptian mathematics. The Egyptians realized that the region of ​​the circle was proportional to its diameter and found the number of 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 hasn’t made any significant progress.

B.C. 600s would be the years when the Persians began to dominate the center east. B.C. By the 550s, Persians are the sole 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, per year 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 a very bright period in science, art and literature. Greek mathematics actually started prior to when 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 famous he went to 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 great pyramid by measuring the size of the shadow of the great pyramid, multiplying this number by the ratio of its length to the length of the current shadow. After time for 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 can be not centered on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the one who is considered 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 up to Babylon by capturing the Persians through 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 school and tried to instruct individuals he gathered around. For political reasons, BC. He left 518 Samos, settled in southern Italy, in the city 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 one another with oath. The 2nd group contains students attending school. Pythagoras school is dependant on number cult. According to them, everything could 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 for example 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 best sides of the right triangle equals the square of the hypotenuse) put the Pythagorean school in a heavy crisis. The discovery of irrational numbers is the initial major crisis of mathematics. Most 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 may be understood from these details, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.