Logarithm Properties | Math

# Logarithm Properties

Logarithm Properties

MATHEMATIC HISTORY

Mathematics is among the oldest sciences in human history. In ancient times, Mathematics was defined while the science of numbers and shapes. Mathematics, like other branches of science, has evolved with time; it is no further possible to describe it in a few sentences. What I’ve to express now will undoubtedly be words that emphasize its various aspects, as opposed to describe mathematics. In one aspect, mathematics is an art like painting and music. A large proportion of mathematicians perform it being an art. From 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 for them could be the depth of the job 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 objective of science may be the universe; If it’s to comprehend, 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. In order 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 view it as a game. Mathematics is just 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 has become far beyond the dimensions any human can rule. Therefore, I do not believe that those who cope with mathematics tend to be more than we understand and perceive it from mathematics than the blind touched net understands and perceives the elephant. The word mathematics, for the very first time, BC. It had been 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 word meaning is “what must be learned”, that’s, information. In the years before these dates, instead of 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. If we take documents which are not based on archaeological findings that require interpretation, but open enough to require interpretation, We can say that it started between 3000 and 2000 in Egypt and Mesopotamia. Based on 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 conclusion of the floods caused by the Nile river each 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 flood, the “geometricists” of their state, who’re responsible for these works, should come to 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 as a result of the measurements and calculations. A second opinion concerning the birth of mathematics is usually the one put forward by Aristotle (384-322 BC). In accordance with Aristotle, mathematics was born in Egypt. But it was created from the boredom of clergymen and priests, not the need for measurement-calculation due to Nile floods. During those times, the only real intellectual class of countries such as Egypt was the priest class. Since the livelihood of the class is given by people or their state, they have much time 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 ;.These two views might be true; priests wanted to simplify the job of the geometric, or they learned just how to calculate the areas of some geometric shapes such as for example triangular and trapezoidal to test that the distribution was fair, and in this way led to the birth of geometry.

We shall divide the written history of mathematics into five periods. The very first period is going to be Egypt and Mesopotamia; this period BC In 2000s BC. It’ll cover a period of 1500-2000 years between 500s. The 2nd period, BC. 500-M.S. It’ll cover an amount 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 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, referred to as the golden age of mathematics, dating from 1700-1900. The period we are residing in, dating back once again to early 1900s, called age modern mathematics, could be the fifth period. I will endeavour to give information regarding the development of mathematics for the reason that period, contributing mathematicians, the spot of mathematics in social life and the basic top features of mathematics for the reason 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 main reasons 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 the fires happened during 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, on average 15-25 meters long and 30-50 inches wide. These leaves were used to write text in place of paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages ​​such as “Paper”, “papier” are derived from the word papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it’s flaky as a result of moisture, heat and similar reasons. Up to now, two papyrus related to mathematics appear to have been hidden under exceptional circumstances. The main resources of our understanding of Egyptian mathematics are these two papyri. The initial of these papyrus is really a 6-meter long and 35-cm wide papyrus referred to as the Ahmes (or Rhind) papyrus. This papyrus, BC. You are a puree written in 2000s, BC. It is 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 book written to instruct math. In the introduction part, after having a few exercises given to teach operations with fractional numbers, 87 questions are made making use of their solutions. They are the kind of questions people can encounter in daily life, such as for instance sharing account, interest calculation, or finding the area of ​​some geometric shapes. That is pretty much our 8th grade mathematics. The next papyrus, referred to 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, with the exception of the two. Are you aware that other two questions, one could be the calculation of the quantity and section of ​​the surface of the sphere part cut by a plane. Another is the question of finding the volume of a pyramid cut by way of a plane. Both questions were solved correctly. Those two questions are accepted since the pinnacle of Egyptian mathematics. The Egyptians realized that the location 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 is understood that Egyptian mathematics has remained as of this level for 2000 years and hasn’t made any significant progress.

B.C. 600s will be the years once the Persians started 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 may be the date that has been accepted as the start of Greek civilization. This date is the beginning 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 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 while and learned geometry in Egypt. While in Egypt, it’s described in books where he calculates the height of the fantastic pyramid by measuring along the shadow of the truly amazing 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 instruct what he learned. It is assumed that abstract proof based on reasoning, that is not based on mathematics – experimental verification, entered into Tales. Additionally, Tales is the one who is known as the very 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 some time, went to Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken up to Babylon by capturing the Persians throughout 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 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’re connected to each other with oath. The second group consists of students attending school. Pythagoras school is founded on number cult. According for them, everything can be reduced to numbers; It comes with 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 known as 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 strong crisis. The discovery of irrational numbers is the very first major crisis of mathematics. Lots of the members of the Pythagorean school were massacred by way of a raid led with a big cyber named Cylon. Pythagoras saved his life, but after many years he died. Pythagoras’thoughts, the Pythagorean school lived for several years under this or that name. As can be understood from this information, Egyptian and Mesopotamian mathematics are the foundation of Greek mathematics.