How to apply the Logarithm rules: product rule, quotient rule, power rule, change of base rule with examples and step by step solutions, summary of the logarithm rules. how to expand logarithmic expression, how to write expressions as a single logarithm
Mathematics is one of many 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 is no further possible to spell it out it in a few sentences. What I’ve to say now will undoubtedly 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 as an art. Out of this point of view, the truth that a work done, a developed theory works in one of the ways or another apart from mathematics does not concern them much. What matters in their mind could be the depth of the work done, the novelty of the methods used, the aesthetic value and the usefulness of mathematics in itself. Mathematics, in another aspect, is really 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 manage 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 have to 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 only a tool for 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 don’t believe people who handle mathematics are far more than we understand and perceive it from mathematics than the blind touched net understands and perceives the elephant. The term mathematics, for the first time, 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 phrase meaning is “what needs to be learned”, that is, information. In the years before these dates, instead of the word mathematics, words that mean geometry, equal 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 based on archaeological findings that want interpretation, but open enough to require interpretation, We can say so it started between 3000 and 2000 in Egypt and Mesopotamia. According to Heredotus (485-415 BC), mathematics started in Egypt. You may already know, 97% of the Egyptian lands aren’t suited to 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 conclusion of the floods caused by the Nile river each year, the boundaries of the landowners’lands become obscure. Since the landowners also pay taxes in proportion to the land they own, after each and every flood, the “geometricists” of the state, who are in charge of these works, should come to take the mandatory measurements and supply the landowners as much land as they’d in the earlier year. Herodotus says that geometry has begun to emerge consequently of those 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 came to be out from the boredom of clergymen and priests, not the requirement for measurement-calculation caused by Nile floods. At that time, the only intellectual class of countries such as for instance Egypt was the priest class. Considering that the livelihood of the class is provided by the public or their state, they have much time for you to share with intellectual pursuits. To 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 ;.Both of these views may 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 test that the distribution was fair, and in this manner led to the birth of geometry.
We will divide the written history of mathematics into five periods. The first period will be Egypt and Mesopotamia; this period BC In 2000s BC. It will cover an amount 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 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 time scale we’re surviving in, dating back once again to the first 1900s, called age modern mathematics, would be the fifth period. I will attempt to give information about the development of mathematics because period, contributing mathematicians, the spot of mathematics in social life and the essential top 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 main reasons for this. The very first is that the ancient Egyptians wrote the writing on papyrus; The second reason is the 3 big fires of the Alexandria libraries, the past of these fires happened during 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, normally 15-25 meters long and 30-50 inches wide. These leaves were used to write text rather than paper after cutting, joining, pressing and undergoing some simple operations. Words in western languages such as “Paper”, “papier” are produced from the word papyrus. The average lifespan of a papyrus is 300 years; 300 years later, it is flaky because of moisture, heat and similar reasons. Up to now, two papyrus linked to mathematics appear to own been hidden under exceptional circumstances. The main sources of our understanding of Egyptian mathematics are those two papyri. The very first of these papyrus is a 6-meter long and 35-cm wide papyrus called the Ahmes (or Rhind) papyrus. This papyrus, BC. You are a puree written in 2000s, BC. It is just 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 instruct math. In the introduction part, after having 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 for instance sharing account, interest calculation, or finding the region 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, is also BC. It is really a booklet written in the 1600s. This papyrus contains 25 questions. These questions are of the type of questions in the Ahmes papyrus, except for the two. When it comes to other two questions, one of them may be the calculation of the quantity and part of the surface of the sphere part cut by a plane. Another may be the question of finding the quantity of a pyramid cut by a plane. Both questions were solved correctly. These two questions are accepted because the pinnacle of Egyptian mathematics. The Egyptians seen 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’s understood that Egyptian mathematics has remained at this level for 2000 years and hasn’t made any significant progress.
B.C. 600s are the years when the Persians started initially to dominate the center 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, per year later, in 479, Greeks expelled the Persians from Greece. This date BC. 479 could be 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 regarded as the father of Greek mathematics. Tales Milet (Aydın) was also born. It is known he went along to Egypt, stayed there for some time and learned geometry in Egypt. During 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 present shadow. After time for Tales Milet, he taught them geometry by forming a group around him to instruct what he learned. It is assumed that abstract proof predicated on reasoning, which is not centered 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 created on the island of Pythagoras Samos (Samos), another father of Greek mathematics. Pythagoras stayed with Tales for a while, visited Egypt following his advice, learned geometry there, visited Egyptian temples, learned religious information, and was taken fully 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 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 folks of this school called “mathematics” live together and they are connected together with oath. The next group consists of students attending school. Pythagoras school is dependant on number cult. According for them, everything can be reduced to numbers; It posseses 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,… will be the fractional numbers that indicate the ratio of the part to the whole. The emergence of irrational numbers with the theorem referred to 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 heavy crisis. The discovery of irrational numbers is the first major crisis of mathematics. Most 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 quite some time under this or that name. As could be understood from this information, Egyptian and Mesopotamian mathematics are the basis of Greek mathematics.