Keep walking and eventually you will wind up where you started. Suppose you start walking due east on the equator. To us the Earth appears to be locally flat, but we know full well that it is not a sheet but a sphere. The Earth has essentially a spherical geometry rather than a flat one- that is, the shortest distance between two points on the Earth’s surface is not a straight line it is a curved path (circle) called a geodesic. If omega is less than one, the universe has negatively curved (hyperbolic) geometry if omega is greater than one, the universe has positively curved (spherical) geometry and if omega is one, the universe has Euclidean (flat) geometry. Omega is related to the density of the universe, which is mass per unit volume of space. One of the consequences of Einstein’s theory of general relativity is that space may be curved or flat depending upon a number we will call omega. The news media has reported extensively about new evidence that the universe is "flat." What does "flat" mean and does that refute Einstein’s contention that the universe is "curved"? September 2000 Vocatio Center for Life Calling and Career. Office of Student Leadership & Engagement.
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