reggio-inspired Archive – Mathematics and Science in SD#38 (Richmond)
Mathematics is among the oldest sciences in human history. In ancient times, Mathematics was defined because the science of numbers and shapes. Mathematics, like other branches of science, has evolved over time; it’s no more possible to explain it in a couple of sentences. What I’ve to state now will soon be words that emphasize its various aspects, rather than describe mathematics. In one aspect, mathematics is an art like painting and music. The great majority of mathematicians perform it being an art. Using this point of view, the fact that a work done, a developed theory works in one way or another besides mathematics doesn’t concern them much. What matters for them could be the depth of the task done, the novelty of the strategy used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really a language. If the goal of science may be the universe; If it is to know, rule and direct everything in the universe, we should have the ability 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 need to know the language of mathematics. In another aspect, mathematics is definitely an intellectual game like chess.
Some mathematicians also notice it as a game. Mathematics is only a tool for 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 do not believe that people who handle mathematics tend to be 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 had been utilized 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 term meaning is “what must 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 is difficult to express anything definite about where and how mathematics started. If we take documents which are not based on archaeological findings that need interpretation, but open enough to require interpretation, We could say so it started between 3000 and 2000 in Egypt and Mesopotamia. According to Heredotus (485-415 BC), mathematics were only available in Egypt. As you know, 97% of the Egyptian lands are not suited to agriculture; It’s the 3% portion that provides life to Egypt and forms the Nile delta. Therefore, these lands are really valuable. However, by the end of the floods due to the Nile river annually, 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 the state, who’re accountable for these works, should arrived at take the required measurements and give the landowners as much land as they’d in the earlier year. Herodotus says that geometry has begun to emerge consequently of the measurements and calculations. An additional opinion concerning the birth of mathematics is the one put forward by Aristotle (384-322 BC). In accordance with Aristotle, mathematics came to be in Egypt. However it was created out of the boredom of clergymen and priests, not the requirement for measurement-calculation caused by Nile floods. At that time, the sole intellectual class of countries such as Egypt was the priest class. Considering that the livelihood with this class is provided by the public or their state, they have much time and energy to give intellectual pursuits. To help 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 these views might be true; priests wanted to simplify the work of the geometric, or they learned how exactly to calculate the aspects of some geometric shapes such as for instance triangular and trapezoidal to check on that the distribution was fair, and this way generated the birth of geometry.
We will divide the written history of mathematics into five periods. The initial 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 next period, BC. 500-M.S. It will cover a period of 1000 years, referred to as the Greek Mathematics period, between 500 years. The third 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 once again to early 1900s, called age modern mathematics, would be the fifth period. I will attempt to offer information about the development of mathematics for the reason that period, contributing mathematicians, the place of mathematics in social life and the fundamental features of mathematics in 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. You will find two major causes for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The second reason may be the 3 big fires of the Alexandria libraries, the past of these 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, typically 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 based on the word papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it’s flaky because of moisture, heat and similar reasons. Up to now, two papyrus linked to mathematics appear to have been hidden under exceptional circumstances. The key sources of our understanding of Egyptian mathematics are those two papyri. The first of those 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 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 guide written to teach math. In the introduction part, following a few exercises given to show operations with fractional numbers, 87 questions receive making use of their solutions. These are the type of questions people can encounter in everyday life, such as sharing account, interest calculation, or finding the region of some geometric shapes. This really is more or less our 8th grade mathematics. The second papyrus, known 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. As for the other two questions, one of them could be the calculation of the amount and area of the surface of the sphere part cut by way of a plane. The other could be the question of finding the amount of a pyramid cut with a plane. Both questions were solved correctly. Both of these questions are accepted because 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 has not made any significant progress.
B.C. 600s will be the years when 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 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 earlier than this period. Two people, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as the daddy of Greek mathematics. Tales Milet (Aydın) was also born. It is famous that he went along to Egypt, stayed there for some time and learned geometry in Egypt. While in Egypt, it is described in books where he calculates the height of the truly amazing pyramid by measuring the length of the shadow of the truly amazing pyramid, multiplying this number by the ratio of its length to the size of 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 based on reasoning, which can be not based on mathematics – experimental verification, entered into Tales. Furthermore, Tales is the one 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, 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 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 time for Samos, he created a college and tried to teach 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 people of this school called “mathematics” live together and they’re connected together with oath. The second group consists of students attending school. Pythagoras school is founded on number cult. According in their mind, 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 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 best sides of the 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. Most of the members of the Pythagorean school were massacred by way of 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 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.