Geometry, the study of space and spatial relationships, is an important and essential branch of the mathematics curriculum at all grade levels. The ability to apply geometric concepts is a life skill used in many occupations. The study of geometry provides the student with a vehicle for enhancing logical reasoning and deductive thinking for modeling abstract problems.
The study of Geometry develops logical reasoning and deductive thinking, which helps us expand both mentally and mathematically. Euclidean Geometry is a branch of mathematics where one must understand the material, and apply the understood material to discover patterns and relationships.
The importance of Euclidean geometry is one of historical and practical use for the study of mathematics in today's society. Euclidean geometry is one of the oldest branches of mathematics, developed by Euclid in 300BC, and serves as the basis of modern mathematics that governs our world.
ReplyDelete"Euclid's Elements written in 300BC, ranks second only to the bible as the most published book in history. It has been studied virtually unchanged to this day, as a geometry textbook and as a model of deductive logic. Euclid listed five axioms that he viewed as general truths and five postulates, which are truths about a particular field. These ten statements and basic rules of logic, serve as a model of deductive reasoning." (Charles D Miller, Vern E Heeren, E John Hornsby Jr. Mathematics Ideas for Memorial University, customedition Harper Collins College Publishers, 1994).
Properties of planes, for example, appear in our daily life. If we are given any three points that are not in a straight line, then a plane can be passed through these points. That is why camera, telescope, and surveying equipment tripods have three legs; no matter how irregular the surface, the tips of these legs determine a plane. On the other hand, if a camera support had four legs, the legs would wobble unless each leg was carefully extended just the right amount. Since the surface of the Earth is not flat, angles play a key role the study of geodesy, the measurement of distances on the Earth's surface. Without such geometric knowledge of angles we would lose an extremely important field of mathematics know as trigonometry. Geometry is a field, which play an important role in the careers of engineers, physicists and mathematicians alike.
Geometry is also used in the early stages of our life, to help develop the mind in determining differences. We all had the game as a child where we must place the different shapes (square, triangles, circles, and so on) in the right slots. These games help us as toddlers to make deductions that in return expand our mind, and are the first exposure to mathematics we as individuals will encounter.
ReplyDeleteGeometry holds a great deal of importance tin fields such as engineering and architecture. For example, many bridges that play an important role in our lives in terms of travel show congruent and similar triangles. These triangles help make the bridge more stable and enables the bridges to withstand great amounts of stress and strain placed on them. In the construction of buildings, geometry can play two roles; one in making the structure more stable and one in enhancing beauty. Geometric shapes can turn buildings and other structures such as the Taj Mahal into great landmarks admired by all. We can use geometry to study such historical landmarks as the leaning tower of Pisa (the leaning bell tower at the cathedral at Pisa), to calculate the angle of its lean and why the structure still stands.
Geometry holds great importance in the forever-expanding world of mathematics. It enables us to picture what is happening in problems we may encounter in the study of mathematics. The study of geometry helps us develop the ability to visualize shapes, volume, area, and so on. Geometric proofs play an important role in the expansion and understanding of many branches of mathematics, from Venn diagrams in set theory to area under the graph in calculus.
One must realize that probably the most important reason a mathematician and/or non-mathematician should understand geometry is the use of deductive thinking and logic. For the mathematician, the use of logic and deductive thinking is important especially in such courses as finite mathematics. For the non-mathematician, logic and deductive reasoning could play a role in doing such courses as Philosophy.
These are reasons why geometry is important in our lives as citizens of the modern world. It is important to understand Euclidean geometry when studying a course because Euclidean geometry does not follow any set pattern. In a course such as calculus, if one knows the pattern or steps to doing a specific type question, then one can easily do these types of questions. But for Euclidean geometry, one can only learn the axioms and results proven from these axioms. The student must apply these axioms with no set pattern or list of steps for solving such problems. Therefore, each problem can have one, two, three, four or infinitely many solutions.
ReplyDeleteWe seem to find aspects of Euclidean geometry everywhere in life. These aspects appear in one's career, in things we take for granted such as bridges, and even the homes we live in. Man used circles and angles to create the sundial, an elementary form of timepiece. The introduction of time made mankind more aware of seasons, age, the concept of motion, and so on. It is important to understand Euclidean geometry even in our entertainment. In such games as pool one uses angles and triangles indirectly to place the balls into the pockets of the pool table. Euclidean geometry is important to understand even for the artist, since most drawings include shapes such as triangles, squares, rhombus, and so on. In modern art these geometric shapes appear as the main concept of the art. So even for artists, an understanding of the very basic concepts of Euclidean geometry is important.
In physics, there is a great deal of importance for the understanding of the aspects of Euclidean geometry. Similar triangles are often used in order to calculate height (similar ratios) and to determine the values of angles (really important in such branches as optics) when solving problems. The use of diagrams, created through the use of knowledge of Euclidean geometry, help the physicist see the details of problems that in return guide him or her to the solutions.
It is extremely important to understand Euclidean geometry because it plays such an important role in our lives. For the engineer and the architect, geometry plays a role in making structures safe and sturdy enough to be able to withstand strains and stress placed on them by nature and man. Besides the practical use of the understanding of Euclidean geometry, it helps us develop deductive reasoning with the use of logic, which helps us expand both mentally and mathematically. Euclidean geometry is a course where one must understand the material, and apply the understood material to questions that may appear in one's mathematical career. Since there is no set pattern when taking on such a problem, it is really important to be able to understand the material. The knowledge in Euclidean geometry also plays an important role in our leisure pleasure, since it is found in children games, pool, and the art world. One can easily see that the concepts of Euclidean geometry directly or indirectly govern our world and our way of thinking about our world. Since our calendar year, for example, is based on one complete revolution of the Earth around the sun (this path is an ellipse), the importance of understanding Euclidean geometry is endless because it plays such an important role governing the aspects of our lives.
ReplyDeleteI'm almost convinced of the importance of geometry ;)
ReplyDeleteDamianne
Thanks for your feedback Damianne.
ReplyDelete