History of Mathematics

History of Math
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Introduction
Mathematics study is a demonstrative discipline that was started with the Pythagoreans in the 6th century BC, and were the people who coined “mathematics” as a term from the ancient Greek mathema, which meant “subject of instruction.” Islamic mathematics was also established and expanded the mathematics acknowledged to these civilizations. Some early examples of counting are considered to date from the 30,000 B.C. which qualifies counting as one of the earliest forms of mathematics. Counting itself was believed to be a simple accounting device that measured or identified quantity. However, the belief is said to be basic, even primitive, that it was not possible to consider it as either a science or subject. In this regard, this paper will provide a portfolio for mathematics history focusing on the content areas, representation of numbers, and proofs surrounding the Pythagoras Theorem, and the irrationality in square root of two.
Part 1: The Content Ares in Math
* Number and Quantity
The description of quantity can be done by use of numbers, for example, 28 pages of reading. The expression of these numbers can be done as fractions, whole numbers, percentages, decimals, and units of measurements like weight, money, length, and time. In addition, the expression of quantities can be done in non-standard units. The Egyptians are believed to be the first people who invented numbers, which they did through a first ciphered numeral system, and the Greeks were second with mapping of counting numbers onto Ionian and Doric alphabets. The discovery of numbers contributed to the origin of Number Theory in the B. Cs, which was done by Euclid of Alexandria. He was an extraordinary mathematician who was also known to many as “the Father of Geometry” and he put forth one of the oldest algorithms recorded as historic.
In mathematics, quantity as a concept is an ancient discovery made in the Aristotle era and earlier. The relationship between quantity and numbers is said to be one in that numbers are used to quantify; meaning, they show or explain the exact amount in form of measurement and counting. The contribution of quantity and numbers in mathematics help to define the actual measure of number in question. For example, quantity is used to determine the number of oranges present in a basket or the number of rotten apples in a basket. In other words, quantity is something such as symbol or number that represents a number on which a mathematical process is achieved. The two types of quantities; magnitude (how much) and multitude (how many), can be divided further as physical and mathematical. In proper understanding, quantities (their order and formal relationships of inequality and equality, proportions, and ratios) are studied by math.
* Algebra
Algebra is recognized as one of the extensive areas in math, in conjunction with geometry and analysis, and number theory. Generally, algebra is understood as the study of mathematical symbols and the rules used in the manipulation of these symbols; it is a uniting thread of just about every aspect in mathematics. Tracing the discovery of algebra goes back to the ancient Babylonians, who were responsible in the development of s system of positional number that greatly helped them in solving of rhetorical algebraic equations. The development of algebraic abstract is traced back in the 19th century, originating from the interest that people had in solving equations, primarily concentrating on what is presently known as Galois theory, and on constructability questions. The originator of axiomatic thinking in algebra and arithmetic was George Peacock.
In the ancient times, the use of algebra was to solve problems and make it easier to find solutions. For example, algebra was used by Babylonians to work out the interest on loans and area of items, among other things. It served an actual purpose and was used efficiently which is why its development was arrived at. it is believed that algebra was first invented in the 9th century after Muhammad ibn Musa al-Khwarizmi, who was a Muslim mathematician, wrote a book he named “Kitab Al-Jabi” from which “Algebra” as a word was derived from. It is believed that Africans contributed to the use of algebra thousands of years ago, thus putting Africa on the limelight as a home of earliest known use of calculation and measuring. Additionally, the continent is believed to be the birthplace of advanced and basic mathematics, and algebra was among the mathematical forms used by Africans in their daily lives.
* Geometry
Geometry is a mathematical branch that deals with properties, measurements, and relationships of lines, solids, surfaces, points, and angles. In other words, geometry is a math that deals with surfaces, shapes, points, ad lines. Arithmetically, geometry is one of the oldest mathematical branches concerned with space properties that relate with shape, distance, size, and relative position of figures, and people who work in geometric fields are known as geometers. It is believed that geometry was started by Euclid, a great mathematician who was known to many as the “Father of Geometry.” The existence of geometry emerged as a field of knowledge that deals with three-dimensional relationships. It was one of the two areas of pre-modern mathematics, the other being the learning of numbers. Classic geometry was emphasized in compass and straightedged structures. The earliest recordings on the start of geometry are traceable back in to the ancient Egypt and Mesopotamia in the 2nd millennium BC.
Africans also played a significant role in the discovery of geometry in that from them discovering the circumference of a circle being approximately three and a half times its diameter, the Sexagesimal System of numeration by which the use of 60 is implemented (for instance, 60 minutes being equals to one degree and 360 degreed making one circle) allowed them to measure heaven and earth in degrees. However, most of the work in the discovery of geometry was done by Euclid who wrote a book he named Elements, which is considered as one of the most outstanding mathematical books written representing the attainment of mathematical revolution. In his book, he includes three geometrical dimensions: spherical, Euclidean, and hyperbolic, which are the only geometries possible for 2-dimensional objects, though the scope of his book provides significant proofs of this.
* Trigonometry
Trigonometry is a mathematical branch that deals with the study of relationships between angles and side lengths of triangles. The emergence of trigonometry happened in the Hellenistic world in the 3rd century BC from geometrical applications to studies related to astronomy. Early studies of triangles were done in the 2nd millennium BC, in Babylonian mathematics and Egyptian mathematics. Trigonometry was predominant in Kushite mathematics as well. A systematic study of the functions of trigonometry started in Hellenistic mathematics, arriving in India as a subdivision of Hellenistic astronomy. In Indian astronomy, the introduction of studies on trigonometric functions performed excellently in the Gupta era, especially because of Aryabhata (sixth century CE), who led to the discovery of the sine function. In the modern perspective, trigonometry started with the Greeks, and Hipparchus was the first person to construct a table of values meant for trigonometric functions.
Being the common culture behind contributing to trigonometry, the ancient Greeks changed it into a methodical science. Astronomy played a major role in the influence of trigonometrical advancements, and most of the first advancements in trigonometry existed in spherical trigonometry on account of its application to astronomy. The Babylonians also used trigonometry when measuring angles, and are said to be among the first people to invent the division of the circle into 360 degrees, but the Greeks were the original pioneers of trigonometry. Since the Greek were the main contributors to trigonometry, three main figures took part in its development: Ptolomy, Hipparchus, and Menelaus. However, other contributors existed as well but as time went by, their contributions have been lost and their names are not recognized, maybe forgotten. It is because if the involvement and contribution of the Greeks to trigonometry that its application is nowadays done into various fields like crime scene investigations, astronauts, architects, engineers, and surveyors.
* Probability
Probability is a mathematical branch that deals with the description of numbers concerning the likelihood of the occurrence of an event, or the likelihood of the truth on proposition. The probability of a number between zero and one, where, roughly speaking, zero is an indication of impossibility of the occurrence of an event, and one indicating the likelihood or certainty. The modern mathematical theory of probability has its roots it attempts of analyzing Gerolamo Cardano’s “games of chance” in the sixteenth century, and by Blaise Pascal and Pierre de Fermat in the seventeenth century (for instance, the problem of points). The origins of probability are traced back in 1654 from a gambler’s dispute concerning the way stakes were distributed between two players whose game was interrupted and never got to finish it. it is because of contemplating a gambling issue posed by Chevalier de Mere in 1654 that contributed to the laying of the fundamental groundwork oof probability theory by Blaise Pascal and Pierre de Fermat who thereby got accredited as the fathers of probability.
Given that probability emerged from gambling, it is applied presently the same way. Such may include the flipping of a coin, throwing a dice, winning a lottery, choosing a card from the deck, pulling a red candy from a back of blue candies, and so on. Additionally, probability may as well be used in predicting the occurrence of certain events other than gambling. For example, climatologists and meteorologists can apply probability to predict the weather based on the patterns and changes in the atmosphere over time. Probability can also be applied when predicting the occurrences of natural disasters, analyzing the result of sporting events, or even getting dressed or buying insurance.
* Statistics
Statistics as a word, came from a modern Latin phrase statisticum collegium, which formed the word statista (Italian word) and the German statistic. It is believed th...