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SpeedFreek
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From Ned Wright's Cosmology FAQ<br /><br /><b>What is meant by a flat Universe?</b><br /><br />The Universe appears to be homogeneous and isotropic, and there are only three possible geometries that are homogeneous and isotropic as shown in Part 3. A flat space has Euclidean geometry, where the sum of the angles in a triangle is 180 degrees. A curved space has non-Euclidean geometry. In a positively curved, or hyperspherical space, the sum of the angles in a triangle is bigger than 180 degrees, and this angle excess gives the area of the triangle divided by the square of the radius of the surface. In a negatively curved or hyperbolic space, the sum of the angles in a triangle is less than 180 degrees. When Gauss invented this non-Euclidean geometry he actually tried measuring a large triangle, but he got an angle sum of 180o because the radius of the Universe is very large (if not infinite) so the angle excess or deficit has to be tiny for any triangle we can measure. If the radius is infinite, then the Universe is flat.<br /><br />According to "Extending the WMAP Bound on the Size of the Universe",<br /><br />"An important question answered by the WMAP mission is that of the curvature of space. The matter and energy density of the Universe indicate that space is very nearly flat. The WMAP data point to a universe with a total energy density within 2% of critical. This means that even if space in not quite flat, the radius of curvature of the Universe is at least of order the size of the observable Universe, and space can be considered to be nearly flat." <div class="Discussion_UserSignature"> <p><font color="#ff0000">_______________________________________________<br /></font><font size="2"><em>SpeedFreek</em></font> </p> </div>