Logarithm Properties | Math

# Logarithm Properties

Logarithm Properties

MATHEMATIC HISTORY

Mathematics is among 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 over time; it is no further possible to explain it in a couple of sentences. What I’ve to say now will soon be words that emphasize its various aspects, rather than describe mathematics. In taking care of, mathematics is an art like painting and music. The vast majority of mathematicians perform it as an art. Using this viewpoint, the truth that a work done, a developed theory works in one way or another apart from 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 a language. If the goal of science is the universe; When it is to understand, rule and direct everything in the universe, we ought to manage 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. In order to understand and interpret them, we must know the language of mathematics. In another aspect, mathematics can be an intellectual game like chess.

Some mathematicians also view it as a game. Mathematics is merely a tool because of its user. After entering it, we understand and perceive what mathematics is inside our knowledge and in the direction of our interest. Mathematics is now far beyond the dimensions any human can rule. Therefore, I do not genuinely believe that people who handle mathematics are far more than we understand and perceive it from mathematics compared to blind touched net understands and perceives the elephant. The word mathematics, for initially, BC. It was used by the members of the Pythagorean school in the 550s. His entry in to the written literature, with Plato BC. It was in the 380s. The phrase meaning is “what must be learned”, that’s, information. In the years before these dates, as opposed to the word mathematics, words which means that geometry, comparable to it in geometry or old languages ​​were used.

It is extremely hard to say anything definite about where and how mathematics started. If we take documents that aren’t predicated on archaeological findings that need 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. You may already know, 97% of the Egyptian lands are not suitable for agriculture; It’s the 3% portion that offers life to Egypt and forms the Nile delta. Therefore, these lands are really valuable. However, at the end 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 the state, who are responsible for these works, should arrive at take the required measurements and give the landowners just as much land as they’d in the previous year. Herodotus says that geometry has begun to emerge consequently of these measurements and calculations. An additional opinion about the birth of mathematics is the one put forward by Aristotle (384-322 BC). In accordance with Aristotle, mathematics was created in Egypt. But it was born out from the boredom of clergymen and priests, not the need for measurement-calculation caused by Nile floods. In those days, the sole intellectual class of countries such as for instance Egypt was the priest class. Considering that the livelihood with this class is supplied by people or their state, they have much time to give to intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of the period, just as others invented games like chess, bridge, and go&hellip ;.These two views might be true; priests desired to simplify the job of the geometric, or they found out just how to calculate the aspects of some geometric shapes such as for instance triangular and trapezoidal to check that the distribution was fair, and in this manner resulted in the birth of geometry.

We shall divide the written history of mathematics into five periods. The first period is going to be Egypt and Mesopotamia; this period BC In 2000s BC. It will cover a period of 1500-2000 years between 500s. The second period, BC. 500-M.S. It’ll cover a period of 1000 years, known as the Greek Mathematics period, between 500 years. The third term, M.S. It’ll 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, known as the golden age of mathematics, dating from 1700-1900. The period we are surviving in, dating back to early 1900s, called age modern mathematics, would be the fifth period. I will endeavour to provide information about the development of mathematics because period, contributing mathematicians, the spot of mathematics in social life and the essential features of mathematics in that period.

We will 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. There are 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 past 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, normally 15-25 meters long and 30-50 inches wide. These leaves were used to publish text as opposed to paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are derived from the phrase 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 possess been hidden under exceptional circumstances. The key sources of our familiarity with Egyptian mathematics are those two papyri. The initial of these papyrus is just a 6-meter long and 35-cm wide papyrus called the Ahmes (or Rhind) papyrus. This papyrus, BC. You’re 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 using their solutions. They are the sort of questions people can encounter in lifestyle, such as sharing account, interest calculation, or finding the region of ​​some geometric shapes. That is pretty much our 8th grade mathematics. The next papyrus, known as the Moscow papyrus and now in the Moscow museum, is also BC. It is really 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 volume and area of ​​the surface of the sphere part cut by a plane. One other may be the question of finding the amount of a pyramid cut with a plane. Both questions were solved correctly. These two questions are accepted whilst 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 is understood that Egyptian mathematics has remained as of 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 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, per year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 is the date which 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 considered to be the father of Greek mathematics. Tales Milet (Aydın) was also born. It is known that he went to Egypt, stayed there for a while and learned geometry in Egypt. While 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 the size of the current shadow. After time for Tales Milet, he taught them geometry by forming friends around him to show what he learned. It is assumed that abstract proof centered on reasoning, which will be not predicated on mathematics – experimental verification, entered into Tales. In addition, Tales is the person who is recognized 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 some time, visited Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken fully 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 returning to Samos, he created a school and tried to show the people 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 are connected to each other with oath. The next group includes students attending school. Pythagoras school is based 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 just 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 right 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 initial major crisis of mathematics. Many of the members of the Pythagorean school were massacred by a raid led with a big cyber named Cylon. Pythagoras saved his life, but after a couple of years he died. Pythagoras’thoughts, the Pythagorean school lived for several years under this or that name. As could be understood from these records, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.