Logarithm Properties | Math

Logarithm Properties

Logarithm Properties

MATHEMATIC HISTORY

Mathematics is one of 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 with time; it’s no longer possible to spell it out it in several sentences. What I’ve to state 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. The great majority of mathematicians perform it being an art. From this standpoint, the fact a work done, a developed theory works in one of the ways or another other than mathematics doesn’t concern them much. What matters in their mind 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 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 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 must know the language of mathematics. In another aspect, mathematics is 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 don’t 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 employed by the members of the Pythagorean school in the 550s. His entry in to the written literature, with Plato BC. It had been in the 380s. The word meaning is “what needs to 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 is extremely hard to state anything definite about where and how mathematics started. When we take documents that are not predicated on archaeological findings that require interpretation, but open enough to require interpretation, We could say so it started between 3000 and 2000 in Egypt and Mesopotamia. In accordance with Heredotus (485-415 BC), mathematics were only available in Egypt. As you 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 extremely valuable. However, at the conclusion of the floods caused by the Nile river each year, the boundaries of the landowners’lands become obscure. Because the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of their state, who are accountable for these works, should come to take the required measurements and provide the landowners just as much land as they’d in the last year. Herodotus says that geometry has begun to emerge as a result of these measurements and calculations. An additional opinion in regards to the birth of mathematics is usually the one put forward by Aristotle (384-322 BC). According to Aristotle, mathematics was born in Egypt. But it was created from the boredom of clergymen and priests, not the requirement for measurement-calculation caused by Nile floods. During those times, the only real intellectual class of countries such as Egypt was the priest class. Considering that the livelihood of the class is supplied by the general public or their state, they’ve much time to share with intellectual pursuits. To help keep them busy, they invented geometry and arithmetic, the mathematics of that time, in the same way others invented games like chess, bridge, and go&hellip ;.These two views may be true; priests desired to simplify the job of the geometric, or they discovered how to calculate the areas of some geometric shapes such as triangular and trapezoidal to test 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 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 second period, BC. 500-M.S. It will cover a period of 1000 years, known as the Greek Mathematics period, between 500 years. The 3rd 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, referred to as the golden age of mathematics, dating from 1700-1900. The time we’re residing in, dating back to the first 1900s, called the age of modern mathematics, will be the fifth period. I will attempt to offer details about the development of mathematics for the reason that period, contributing mathematicians, the place of mathematics in social life and the basic features of mathematics for the reason that period.

We shall 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 will find two main reasons for this. The foremost is that the ancient Egyptians wrote the writing on papyrus; The next reason could be the 3 big fires of the Alexandria libraries, the past of the fires happened through 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 publish 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 term papyrus. The common lifespan of a papyrus is 300 years; 300 years later, it is flaky because of moisture, heat and similar reasons. To date, two papyrus related to mathematics appear to possess been hidden under exceptional circumstances. The key resources of our knowledge of Egyptian mathematics are both of these papyri. The very 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 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 book written to show math. In the introduction part, after having a few exercises given to show operations with fractional numbers, 87 questions are given making use of their solutions. These are the kind of questions people can encounter in everyday life, such as sharing account, interest calculation, or finding the area of ​​some geometric shapes. This really is just about our 8th grade mathematics. The next papyrus, referred to as the Moscow papyrus and now in the Moscow museum, can be BC. It is a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the type of questions in the Ahmes papyrus, with the exception of the two. Are you aware that other two questions, one is the calculation of the amount and area of ​​the surface of the sphere part cut by way of a plane. Another is the question of finding the quantity of a pyramid cut by way of a plane. Both questions were solved correctly. Those two questions are accepted as the pinnacle of Egyptian mathematics. The Egyptians seen that the location 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 sole 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, a year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 may be the date that was accepted as the start of Greek civilization. This date is the start of a really bright period in science, art and literature. Greek mathematics actually started sooner than this period. Two different people, Tales (624-547 BC) and Pythagoras (569-475 BC), are regarded as the father of Greek mathematics. Tales Milet (Aydın) was also born. It is known that he visited Egypt, stayed there for a time and learned geometry in Egypt. While in Egypt, it is described in books where he calculates the height of the great pyramid by measuring the length of the shadow of the great pyramid, multiplying this number by the ratio of its length to along the current shadow. After time for Tales Milet, he taught them geometry by forming friends around him to instruct what he learned. It’s assumed that abstract proof centered on reasoning, which can be not based on mathematics – experimental verification, entered into Tales. In addition, Tales is the person who is known as the very first philosopher in human history. He came to be on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for a 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 returning to Samos, he created a school and tried to show the folks 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 together with oath. The 2nd group contains students attending school. Pythagoras school is based on number cult. According in their mind, everything may be reduced to numbers; It posseses 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,… will be the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem called 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 heavy crisis. The discovery of irrational numbers is the first major crisis of mathematics. Many of the members of the Pythagorean school were massacred with a raid led by a big cyber named Cylon. Pythagoras saved his life, but after a few years he died. Pythagoras’thoughts, the Pythagorean school lived for several years under this or that name. As can be understood from these records, Egyptian and Mesopotamian mathematics are the cornerstone of Greek mathematics.