H. E. Smith  Winter 2007 
Physics 7  Lecture Summary #19 Cosmology: The Structure & Future of the Universe 
First, there are probably some questions on your mind:
The Geometry of the Universe
General Relativity allows for three geometries of Spacetime in the Universe depending on the density of the Universe and the Universal fate:
Hyperbolic (Open) Geometry
Flat (Euclidean) Geometry
Spherical (Closed) Geometry

We Live in a Curved Space
Before you go off thinking that this is all to wierd to try
to grasp, remember that we live on a spherically curved surface, called Earth.
Lines of longitude, parallel at the equator, follow the surface of the
Earth, converging at the poles.
Also, circles may not be what they seemed in high school geometry. Suppose
you started drawing circles around
the North Pole, keeping the pole at the center. Measuring the relation between
Circumference and radius, you would find that for small circles:
(Space always seems flat on small scales; that's why there are still people who believe the Earth is flat!). But continuing to draw ever increasing circles (lines of latitude) you will finally draw the biggest circle that you can on the earth  around the equator. Now the circumference of the circle is the circumference of the Earth. The radius, measured along the curved surface from the pole to the equator is 1/4 of the circumference of the earth:  © Edward L. Wright (UCLA), used with permission. 
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