The period 213 BCE to 1425 CE, are characterized by the beginning of a gradual ceasing of the isolation of China and India to the outside world. Due to natural boundaries (mountains, seas and deserts) providing the isolation, mathematics in India and China were almost developed independently during the ancient era. It was the Silk Road, began during the Han dynasty (206 BCE – 220 CE), that opened up communication between the West and Southern and Eastern Asia. With this communication, cultures and ideas moved, including mathematical knowledge, allowing undiscovered concepts to enter and discovered concepts to be leave, developed elsewhere and re-enter further advanced. One thing we can be sure is that by the opening of our period, mathematics has already been discovered in both places and were well underway in development.
The first year of the period, 213 BCE, is infamous for Emperor Shi-huang’s command for the burning of all books not officially sanctioned in the Qin Empire. As a result, it is difficult to obtain precise record of mathematics during the Qin dynasty. However, we do see some of the greatest endeavours in human history in the building of the terracotta army’s tomb and the Great Wall of China, both of which require advanced mathematical knowledge, especially geometrical formulas, to architect. This proves that constructional mathematics reached a new unparalleled height in the world at the time. In the attempt to unite the conquered states under the Qin empire, standard weight system was also implemented empire-wide. Meanwhile in India, we see what is referred to as Jaina mathematics period. Whereas ancient time Indian mathematics was mostly intended to build for religious and ritualistic purposes, Jaina mathema...
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...Retrieved from University of St. Andrews Web site: http://www-history.mcs.st-andrews.ac.uk/HistTopics/Nine_chapters.html
O'Connor, J. J., & Robertson, E. F. (2003, December). Overview of Chinese mathematics. Retrieved from University of St. Andrews Web site: http://www-history.mcs.st-andrews.ac.uk/HistTopics/Chinese_overview.html
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Abstract: This paper gives an insight into the Mathematics used by the American Indians. The history of American Indians and how they incorporated mathematics into their lives is scarce. However from the information retrieved by Archeologists, we have an idea of the type of mathematics that was used by American Indians.
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They constructed the 12-month calendar which they based on the cycles of the moon. Other than that, they also created a mathematical system based on the number 60 which they called the Sexagesimal. Though, our mathematics today is not based on their system it acts like a foundation for some mathematicians. They also used the basic mathematics- addition, subtraction, multiplication and division, in keeping track of their records- one of their contributions to this world, bookkeeping. It was also suggested that they even discovered the number of the pi for they knew how to solve the circumference of the circle (Atif, 2013).
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.
Between 1850 and 1900, the mathematics and physics fields began advancing. The advancements involved extremely arduous calculations and formulas that took a great deal of time when done manually.
The abstractions can be anything from strings of numbers to geometric figures to sets of equations. In deriving, for instance, an expression for the change in the surface area of any regular solid as its volume approaches zero, mathematicians have no interest in any correspondence between geometric solids and physical objects in the real world. A central line of investigation in theoretical mathematics is identifying in each field of study a small set of basic ideas and rules from which all other interesting ideas and rules in that field can be logically deduced. Mathematicians are particularly pleased when previously unrelated parts of mathematics are found to be derivable from one another, or from some more general theory. Part of the sense of beauty that many people have perceived in mathematics lies not in finding the greatest richness or complexity but on the contrary, in finding the greatest economy and simplicity of representation and proof.