Geometry
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    Geometry is the area of math that deals with objects and the areas that they occupy.  It is described within many different classifications.  The first of these classifications is analytical geometry.  It is the kind of geometry that a student would learn in his or her school, for example.  Analytical geometry says that straight lines, curves, and geometric figures are represented with algebraic expressions.  In analytical geometry, a straight line is always represented by two variables, x and y.  Analytical geometry is important because without it, non-Euclidian geometry would not have been possible.  It also affected calculus and other advanced fields of mathematics.  Then, in 1637, a French philosopher and mathematician named Rene Descartes wrote a book named A Discourse on Method.  In his book, he showed a link between geometry and algebra.

    Another classification of geometry is descriptive geometry.  Descriptive geometry is the art of drawing 2-D figures or representations of 3-D figures and solving problems relating to the size and space of figures.  Engineering and architectural drafting are greatly based on descriptive geometry.

    Non-three dimensional geometry is based on the thought that the universe is made up of an infinity of spheres.  This idea started when mathematicians started thinking about the possibility of there being more than three dimensions.  The four dimensions are: the x axis, the y axis, the z axis, and the radius of the sphere.  Basically, the four dimensions are how wide (x), how tall (y), how thick (radius), and where it starts (z).

    Geometry was slowly becoming important in the ancient world because a long time ago, people were worried about accurately measuring right angles in the corners of fields and buildings.  Pythagoras tried to solve this problem.  He proved that there were certain laws that were always true, for example, "a straight line is the shortest distance between two points" and "the sum of the interior angles of any triangle equals 180 degrees".

    After Pythagoras, there was a brilliant man named Euclid who was deeply interested in Geometry.  Euclid wrote Elements, which is a textbook with geometry rules.  Elements is often used today by many students and scholars.  Euclid paved the way for Archimedes, a Greek scientist.  Archimedes found ways to measure areas of curved shapes.  He also discovered how to find surface areas and volumes of shapes such as paraboloids and cylinders.  Last but not least, Archimedes discovered Pi, and he determined that it was between 3 ¹⁰/₇₀ and 3 ¹⁰/₇₁.

    The Great Wall of China could not have been built without the numerous laws of Geometry.  Geometry was mainly used by the Chinese in the building of the wall because the wall is actually a huge amount of triangles put together to form one great structure.  The reason for this is because triangles are much more sturdy than most other shapes, such as squares.  Also, the Chinese must have measured how long, wide, and/or tall the wall would be in order to estimate the amount of bricks, labor, and money that would be needed.  If they had not used geometry in this scenario, the Chinese could have either not used enough money and not had enough labor, or spent too much unnecessary money.  A third way that the Chinese used geometry to build the wall was because they had to be able to know whether or not the wall was going to be able to sustain its structural integrity in certain places due to extreme angles.  Without geometry, the building of the Great Wall of China would have been a disaster.

This Page was last edited on Thursday, July 27, 2000 .

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