History of Mathematics, Research Paper Example

Introduction

Understanding the history, traditions and development of mathematics has several advantages. Before starting the class, I had some knowledge about the mathematical knowledge of Egyptians and Greek philosophers, however, this knowledge was not extensive. I did assume that for building geometrically symmetrical buildings and achieving an almost unbelievable accuracy compared to the size of the pyramids had to be built on mathematical knowledge. Still, the class and the whole course opened my eyes about the beliefs of ancients about the connection between natural and rational world, as well as philosophy. As ancient Greek used mathematical rules to explain philosophical and emotional effects.

The Ancient History of Numeration Systems and Mathematics

Egyptian, Babylonian, Mayan, Hindu, Arabic, Greek, and Chinese Numeration Systems. One of the most commonly known mathematical achievement in the Ancient world is the building of Egyptian pyramids. Egyptian mathematics were based on hieroglyphs that signposted each number. They did work out equation, constants and developed the “Golden Ratio” which was used during the building of the pyramids. The base of the pyramid is a square of a pre-determined size, and there are indications that the Egyptians planned the angle of the slope as well.

Babylonians possessed an advanced number system, while they, just like Egyptians divided the day into 24 hours and hours to 60 minutes. They also developed tables that contained numbers squared up to 59. Also, according to tablets survived until today, Babylonians were aware of the theory of Pythagoras.

The Mayan ancient civilization had signs for numerals, advanced calendars and methods to work out the position of the planets based on time and their orbit. They also had a base 20 system developed, and only used three symbols to note down numbers. Interestingly, they had two different calendars: one consisting of 260 days and 13 months named after their mythological gods. The second calendar was closer to today’s official one: consisting of 365 days and 18 months. However, the accuracy of these calendars indicates that the Mayans found effective ways of measuring time, position of the planets and length of days.

Hindus, on the other hand, had several contributions towards the development of mathematics. They discovered square roots, quadratic equations, trigonometry functions and knew about the complexity of Zero. They also later, in the 7^th Century BC discovered irrational numbers and negative numbers were analyzed around 2-300 BC.

Arabic numbers are the basis of today’s mathematical systems in the West. Al-Khwarizmi was the first in the Arabic civilization to study algebra. The Arabic developed different types of counting, reckoning and decimals.

Chinese early mathematicians discovered the right methods for counting, geometrical rules and working with fractions. The right-angle triangle was also studied by them, included in the hsuan-thu diagram, which describes the exact same rule as the Pythagorean theorem.

Fibonacci and the golden ratio. The rule of Fibonacci tells us that the longer part divided by the shorter one is the same as the whole length divided by the longer part. Creating a golden ratio did require abstract and complicated way of thinking. The golden ratio is used in modern architecture, as well as artists in Greece. The Pantheon is based on the Golden Ratio, that is why it is so pleasing for the eye, however, its exact measurements are not intentional. The actual value of the Golden Ratio is an irrational number, around 1.61. Going further, Fibonacci also created a sequence, called Fibonacci Sequence.

The Contribution of Euclid towards Modern Mathematics. Euclid presented the so called number theory, and created the definition of numbers. According to him, a number is a multitude of different units. He also defined prime numbers, which can only be defined by themselves. Euclid also created a simple method for finding the largest common divisor, something that is still taught today in advanced mathematics classes. He also created the theory of “perfect numbers”.

Archimedes: the Father of Mathematics. Archimedes, through his physical laws discovered, made a great contribution towards the discovery of levers. He also created a new mathematical and number system, as he was not happy with the existing Greek one. In geometry, he discovered the simple way to measure the area of complex shapes, called the “complex calculus”, a method that measures the area of different rectangles and adds the area together. This method was useful for planning, building and measuring objects. Further, he discovered a method for measuring the circle, the parabola, as well as developed a reckoning method, called the “sand reckoner”.

Conclusion

It is impossible to look at the theories and techniques of modern mathematics without understanding their ancient origins. It is indeed extremely surprising to see that, compared to the dark medieval era in Europe, ancients were more advanced in mathematics, physics, building and geometry. The fact that different ancient civilizations constantly learned from each other and developed their theories, approaches, numbers systems and calculations further makes people feel grateful for the contribution. Without Archimedes, the Ancient Mayan and Egyptians, we should have started the quest for revealing the secret behind numbers over again.