Spherical Geometry. Through a given point not on a line, there are no lines parallel to the given line. Lines are represented by curves on the great circles.

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Presentation transcript:

Spherical Geometry

Through a given point not on a line, there are no lines parallel to the given line. Lines are represented by curves on the great circles of the sphere.

Assume that the following figure is a sphere. Lines are represented by curves on the great circles of the sphere. Note that they are curved outward, so the sum of the angles will be greater than 180 o.

Basketball Activity What actually comprises the sphere? What is a “line” on a sphere? The intersection of two distinct lines is: parallel lines? Are there parallel great circles on a sphere?

On the Earth what is the only latitude that forms a great circle? How do all the other latitudes compare to a great circle of the Earth? Which longitude lines on the Earth are great circles? Where do all longitude lines on the Earth intersect? The points at the opposite ends of a sphere are called antipodal points. Given the name of two.