The study of points, lines, planes, shapes, and space

 “Father of Geometry”  Greek mathematician  Discovered the basics of Euclidean geometry as we know it in the mid 3 rd century.

 What we will be learning in this class.  The study of flat space.  Also called “plane geometry”  Important characteristics  Shortest distance between two points is a straight line  All triangles have exactly 180   The concept of perpendicular to a line can be illustrated as seen in the picture at the right.

 The study of curved surfaces  There are many different types of non-Euclidean geometry  In curved space, the sum of the angles of any triangle is not always equal to 180°.  On a sphere, there are no straight lines. As soon as you start to draw a straight line, it curves on the sphere.  In curved space, the shortest distance between any two points (called a geodesic ) is not unique.  In curved space, (for spherical (riemannian) or hyperbolic geometry)the concept of perpendicular to a line can be illustrated as seen in either of these pictures.