Students' Contributions: Euclidean Geometry (by 9B Henry Chen)

Euclidean Geometry is the study of the properties of Euclidean space. Euclidean is the adjective of Euclid. Euclid is a mathematician in Greek, as known as Euclid the Alexandria. Often time people referred him "Father of Geometry". His book, Element, is one of the most significant and influential book in the history of mathematic. Euclidean Geometry is the principle in Element. Basically, Euclidean space is the Euclidean plane and three-dimensional space of Euclidean geometry. So, Euclidean geometry is made out of several basic postulates that has a dramatic influence on the later development of geometry. The property of Euclidean Geometry also reveals itself as a axiomatic system, which the statements are all true. Here are the postulates of Euclidean geometry in the book Element:

1.    To draw a straight line from any point to any point. - The statement means that a straight line can be drawn from on given point to another.2.    To produce [extend] a finite straight line continuously in a straight line. - The statement means that both ends on a single line can be extended endlessly.
3.    To describe a circle with any center and distance [radius]. - the statement means that a circle contains a center and all the points from the center with the same distance(radius) are joined to form a circle.
4.    That all right angles are equal to one another.
5.    The parallel postulate: That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. - The statement means that the if two line is crossed by a transversal and the lines are parallel, then the same-side interior angles will be supplementary. If the angles are not supplementary and the sum is less than 180 degree, then the two lines will intercept at a certain point on the side of the angles.