Logarithm Properties | Math

Logarithm Properties

Logarithm Properties

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 over time; it’s no more possible to spell it out it in a couple of sentences. What I’ve to state now will be words that emphasize its various aspects, as opposed to describe mathematics. In one aspect, mathematics is an art like painting and music. The great majority of mathematicians perform it as an art. Using this perspective, 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 in their mind could be the depth of the task done, the novelty of the techniques 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 must 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 definitely an intellectual game like chess.

Some mathematicians also see it as a game. Mathematics is just a tool for its user. After entering it, we understand and perceive what mathematics is in your 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 those that cope with mathematics are more than we understand and perceive it from mathematics compared to blind touched net understands and perceives the elephant. The phrase mathematics, for the very first time, BC. It had been employed by the members of the Pythagorean school in the 550s. His entry to the written literature, with Plato BC. It had been 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’s not possible to express anything definite about where and how mathematics started. If we take documents that aren’t based on archaeological findings that want interpretation, but open enough to require interpretation, We are able to 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 aren’t suitable for agriculture; It is the 3% portion that offers life to Egypt and forms the Nile delta. Therefore, these lands are incredibly valuable. However, at the end of the floods caused by 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 their state, who’re responsible for these works, should come to take the required measurements and give the landowners the maximum amount of land as they’d in the last year. Herodotus says that geometry has begun to emerge as a result of these measurements and calculations. Another opinion about the birth of mathematics is the main one put forward by Aristotle (384-322 BC). Based on Aristotle, mathematics came to be in Egypt. But it came to be out 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 for instance Egypt was the priest class. Since the livelihood with this class is provided by people or their state, they have much time for you 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 ;.Both these views might be true; priests wanted to simplify the job of the geometric, or they discovered how to calculate the areas of some geometric shapes such as for example triangular and trapezoidal to check on that the distribution was fair, and this way resulted in the birth of geometry.

We will divide the written history of mathematics into five periods. The very first period will undoubtedly be Egypt and Mesopotamia; this period BC In 2000s BC. It will cover a period of 1500-2000 years between 500s. The 2nd period, BC. 500-M.S. It will cover a period of 1000 years, called the Greek Mathematics period, between 500 years. The next 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, called the golden age of mathematics, dating from 1700-1900. The time we are residing in, dating back again to early 1900s, called age modern mathematics, would be the fifth period. I will try to provide information about the development of mathematics in that period, contributing mathematicians, the area of mathematics in social life and the essential 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 main reasons for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The next reason is the 3 big fires of the Alexandria libraries, the last of the fires happened during the conquest of Egypt by 641 Muslims, the written documents disappeared. Papyrus may 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 rather than 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 average lifespan of a papyrus is 300 years; 300 years later, it’s flaky because 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 knowledge of Egyptian mathematics are those two papyri. The very first of the papyrus is 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 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 instruct math. In the introduction part, after having a few exercises given to show operations with fractional numbers, 87 questions are made using their solutions. They’re the sort of questions people can encounter in lifestyle, such as for instance sharing account, interest calculation, or finding the location of ​​some geometric shapes. That is pretty much our 8th grade mathematics. The second papyrus, called 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 kind of questions in the Ahmes papyrus, with the exception of the two. Are you aware that other two questions, one of them is the calculation of the quantity and section of ​​the surface of the sphere part cut by way of a plane. Another is the question of finding the volume of a pyramid cut with a plane. Both questions were solved correctly. These two questions are accepted while 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 as of this level for 2000 years and hasn’t made any significant progress.

B.C. 600s would be the years once the Persians started initially to dominate the center east. B.C. By the 550s, Persians are the only real 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 may be the date that has been accepted as the beginning of Greek civilization. This date is the start of an extremely bright period in science, art and literature. Greek mathematics actually started prior to when this period. A couple, 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 visited Egypt, stayed there for a time and learned geometry in Egypt. During Egypt, it is described in books where he calculates the height of the truly amazing 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 time for Tales Milet, he taught them geometry by forming friends around him to instruct what he learned. It is assumed that abstract proof centered on reasoning, which can be not centered on mathematics – experimental verification, entered into Tales. Additionally, Tales is the one who is considered 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 fully 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 time for Samos, he created a college and tried to show 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 individuals of this school called “mathematics” live together and they are connected to each other with oath. The 2nd group contains students attending school. Pythagoras school is based on number cult. According for them, everything can be reduced to numbers; It has 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,… are 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 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. Many of the members of the Pythagorean school were massacred by a raid led by way of a big cyber named Cylon. Pythagoras saved his life, but after a few years he died. Pythagoras’thoughts, the Pythagorean school lived for quite some time under this or that name. As may be understood from these records, Egyptian and Mesopotamian mathematics are the basis of Greek mathematics.