ROLE AND APPLICATION OF MATHEMATICS AS A TOOL
IN SOLVING ENGINEERING PROBLEMS
TABLE OF CONTENTS
Historical Development 4
Role and Application of Mathematics as a Tool in
Solving Engineering Problems
Euclid of Alexandria 7
RenÃ© Descartes 10
The objective of this project is to determine the role and application of mathematics as a tool in solving engineering problems. In other words, the goal is to prove the importance of mathematics and its benefits when applied to challenges that may arise out of everyday ...view middle of the document...
Ancient societies used a variety of methods to either estimate or guess the solutions to problems in their daily lives. These problems fuelled the need for mathematical concepts which inevitably led to the development of [pic]numbers.
The Sumerians, Babylonians and, the ancient Egyptians were the first mathematicians and by extension the first highly skilled scientists. They developed the use of [pic]numbers beyond the basic tasks of counting to solving the practical problems of building, agriculture, and astronomy. The more complex their lives became, the more important were their abilities to do calculations. Egyptian mathematics was primarily arithmetic, with an emphasis on measurement, surveying, and calculation in geometry. The beginning of geometry can be traced to ancient Mesopotamia, Egypt, and the Indus Valley. Geometry was initially a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were utilized to meet practical needs in surveying, construction and astronomy as well as various crafts. The Egyptian Rhind Papyrus, the Moscow Papyrus and the Babylonian clay tablets are some of the earliest known texts in history which entails the use of geometry.
One of the marvels in the use of geometry is the Great Pyramid of Khufu built by the Egyptians with great geometric precision. It contains a near perfect square base of 230 meters that differ from each other by less than 20 centimeters, while the right angles have an error of less than 1/27,000. Even the angles of the slopes were calculated to near perfection at 51 degrees each.
Ancient clay tablets also reveal that the Babylonians used geometry including the Pythagorean relationships. One clay tablet reads:
â€œ4 is the length and 5 the diagonal. What is the breadth? Its size is not known. 4 times 4 is 16. 5 times 5 is 25. You take 16 from 25 and there remains 9. What times what shall I take in order to get 9? 3 times 3 is 9. 3 is the breadth.â€
As mathematics progressed through history, Ancient Greeks practiced centuries of experimental geometry furthering the discoveries made by Egyptians and Babylonians. They fashioned the first formal mathematics of any kind by organizing geometry with rules of logic. Many ancient individuals contributed to the subject but none were equivalent to the impact of Euclid and his Elements of geometry. Euclidâ€™s Elements (c. 300BC) was so absolute and clearly written that it completely influenced the work of his predecessors (Euclidian geometry).
In the Middle Ages mathematics was further developed in medieval Islam by contributions to the development of geometry, especially in algebraic geometry and geometric algebra. The idea of reducing geometrical problems such as duplicating the cube to problems in algebra was conceived by Al-Mahani. ThÄbit ibn Qurra (836-901) was an Arab astronomer, mathematician and physician who analysed arithmetical operations applied to ratios of geometrical...