Since the sun was so far away, Eratosthenes reasoned that the sun's rays could be considered parallel, so that at noon of the summer solstice, a line through the well in Syene would continue through the center of the earth. The student understands the structure of, and relationships within, an axiomatic system. The student compares and contrasts the structures and implication of Euclidean and non-Euclidean geometries. Clarifying Activity Students explore a non-Euclidean geometry and explain the differences between it and Euclidean geometry. Spherical geometry is used as an example below.
Spherical geometry consists of all the points on the surface of a sphere.
Using a globe, we can illustrate the definition of a spherical line. The equator and other longitudinal lines are examples of great circles on a sphere, or spherical lines. Note that latitudinal lines are not actual lines on a sphere because their centers are not the center of the sphere. You can use string to help find a great circle of a sphere by pulling it tight, like a belt, around the sphere. If the circle is not a great circle the string will slip off the sphere.