Geometry - Admission/Application Essay Example

Geometry Geometry is a branch of mathematics that deals or attempts to explain and describe the shape, size, or relative position of an object in space. The study of geometry dates back to the time of ancient Greek. The Euclidian geometry for example originated in the 6th century and it laid the foundation for modern geometry. Currently, the study has advanced to include other branches of mathematics such as number theory, algebra, and topology. Riemannian geometry for example is among the latest braches of geometry.

Each of the above fields of specialization has a different approach to the study of geometry (Mlodinow, 2002). Indeed, a good mathematician will view the different branches of geometry as mere tools designed to enable mathematicians describe and find solutions to mathematical problems more easily rather than a source of contradiction. Geometry applies well-known aspects that have evolved into distinctive area of study. They include vectors, coordinate systems, and transformation/ mappings. Each of these perspectives can be used to explain geometry problems.

For example finding the area of a rectangle can be explained using either of the above. The problem can be explained as a vector problem, where the area will be defined as the cross product of vectors a, b (where a, b are the sides of the rectangle). Thus, the area of the square will be given by, where a, b be are the respective vectors that define each side a and b. Thus, area will be the product of the magnitude of the two vectors multiplied with the Sine of the angle between them. Since the angle between the two vectors is 90 degree, the sine becomes one.

Further, the problem can be viewed as a coordinate problem whereby, the area is described as the sum of the squares that are enclosed by the lines A and B. In this case, the area would be described as the distance between the coordinates that describes the square. Thus, the area would determine as a product of distances separating respective magnitudes under each of the respective coordinates that describes the square.Lastly, the problem of finding the area of a rectangle can be viewed as a transformation problem.

Let a, b be the two sides of a unit square located in the first quadrant of a two-dimensional coordinate system. Then the area of any other square will be the transformation of the initial unit square. The actual area will then be given by a transformation coefficient multiplied by the area of the unit square (Mlodinow, 2002). In this case, the coefficient of transformation will be determined by the nature of the transformation. For instance if we are considering a magnification, then the area would be described as the coefficient of magnification multiplied by the area of the basis square.

Similarly, a series of transformations such as rotation, followed by magnification would have a resultant coefficient of transformation that will determine the resultant area. In conclusion, geometry problems can be solved from different approaches and perspectives. Nevertheless, physical phenomenon such as size, position, and orientation studied in geometry are invariant under change of coordinate systems of computational approach. ReferenceMlodinow, M. (2002). Euclids window (the story of geometry from parallel lines to hyperspace), London: Allen Lane.