1. All article from Shape of the Universe, WMAP website at NASA.

2. local geometry, which relates especially to the curvature of the universe, especially in the observable universecurvature global geometry, which relates to the topology of the universe as a whole, measurement of which may not be within our ability. Consideration of the shape of the universe can be split into two:

3. curvature

4. Local geometry (spatial curvature) The local geometry is the curvature describing any arbitrary point in the observable universe (averaged on a sufficiently large scale). Many astronomical observations, such as those from supernovae and the Cosmic Microwave Background (CMB) radiation, show the observable universe to be very close to homogeneous and isotropic and infer it to be accelerating. The local geometry is the curvature describing any arbitrary point in the observable universe (averaged on a sufficiently large scale). Many astronomical observations, such as those from supernovae and the Cosmic Microwave Background (CMB) radiation, show the observable universe to be very close to homogeneous and isotropic and infer it to be accelerating. arbitrary: random Homogeneous: same quailty Isotropy: is uniformity in all orientations

5. Possible local geometries There are three categories for the possible spatial geometries of constant curvature, depending on the sign of the curvature. If the curvature is exactly zero, then the local geometry is flat; if it is positive, then the local geometry is spherical, and if it is negative then the local geometry is hyperbolic. There are three categories for the possible spatial geometries of constant curvature, depending on the sign of the curvature. If the curvature is exactly zero, then the local geometry is flat; if it is positive, then the local geometry is spherical, and if it is negative then the local geometry is hyperbolic. Under the assumption that the universe is homogeneous and isotropic, the curvature of the observable universe, or the local geometry, is described by one of the three "primitive" geometries (in mathematics these are called the model geometries): Under the assumption that the universe is homogeneous and isotropic, the curvature of the observable universe, or the local geometry, is described by one of the three "primitive" geometries (in mathematics these are called the model geometries): a. 3-dimensional Flat Euclidean geometry, generally notated as E3 b. 3-dimensional spherical geometry with a small curvature, often notated as S3 c. 3-dimensional hyperbolic geometry with a small curvature Hyperbolic: exaggerating

6. Global geometry Global geometry covers the geometry, in particular the topology, of the whole universe—both the observable universe and beyond. While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. For this discussion, the universe is taken to be a geodesic manifold, free of topological defects; relaxing either of these complicates the analysis considerably. Global geometry covers the geometry, in particular the topology, of the whole universe—both the observable universe and beyond. While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. For this discussion, the universe is taken to be a geodesic manifold, free of topological defects; relaxing either of these complicates the analysis considerably. study of global geometry are whether the universe: study of global geometry are whether the universe: a. Is infinite in extent or, more generally, is a compact space; b. Has a simply or non-simply connected topology. Topology (from the Greek τόπος, “place”, and λόγος, “study”) is a major area of mathematics concerned with the most basic properties of space, such as connectedness. geodesic is a generalization of the notion of a "straight line" to "curved spaces". Infinite: limitless

7. FLRW model of the universe In General Relativity, this is modeled by the Friedmann–Lemaître– Robertson–Walker (FLRW) model. This model, which can be represented by the Friedmann equations, provides a curvature (often referred to as geometry) of the universe based on the mathematics of fluid dynamics, i.e. it models the matter within the universe as a perfect fluid. Although stars and structures of mass can be introduced into an "almost FLRW" model, a strictly FLRW model is used to approximate the local geometry of the observable universe. In General Relativity, this is modeled by the Friedmann–Lemaître– Robertson–Walker (FLRW) model. This model, which can be represented by the Friedmann equations, provides a curvature (often referred to as geometry) of the universe based on the mathematics of fluid dynamics, i.e. it models the matter within the universe as a perfect fluid. Although stars and structures of mass can be introduced into an "almost FLRW" model, a strictly FLRW model is used to approximate the local geometry of the observable universe. Another way of saying this is that if all forms of dark energy are ignored, then the curvature of the universe can be determined by measuring the average density of matter within it, assuming that all matter is evenly distributed (rather than the distortions caused by 'dense' objects such as galaxies). Another way of saying this is that if all forms of dark energy are ignored, then the curvature of the universe can be determined by measuring the average density of matter within it, assuming that all matter is evenly distributed (rather than the distortions caused by 'dense' objects such as galaxies).

8. How to calculate the shape of the universe http://icosmos.co.uk/index.html http://icosmos.co.uk/index.html http://icosmos.co.uk/index.html

9. Many kinds of universe 1. Flat universe 2. Spherical universe 3. Hyperbolic universe 4. Spherical Expanding Universe 5 ……. From Jonathan Strickland http://science.howstuffworks. com/dictionary/astronomy- terms/space-shape2.htm http://science.howstuffworks. com/dictionary/astronomy- terms/space-shape2.htm

10. Will the Universe expand forever? The fate of the universe is determined by a struggle between the momentum of expansion and the pull of gravity. The rate of expansion is expressed by the Hubble Constant, Ho, while the strength of gravity depends on the density and pressure of the matter in the universe. If the pressure of the matter is low, as is the case with most forms of matter we know of, then the fate of the universe is governed by the density. If the density of the universe is less than the "critical density" which is proportional to the square of the Hubble constant, then the universe will expand forever. If the density of the universe is greater than the "critical density", then gravity will eventually win and the universe will collapse back on itself, the so called "Big Crunch". However, the results of the WMAP mission and observations of distant supernova have suggested that the expansion of the universe is actually accelerating which implies the existence of a form of matter with a strong negative pressure, such as the cosmological constant. This strange form of matter is also sometimes referred to as "dark energy". If dark energy in fact plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever. The fate of the universe is determined by a struggle between the momentum of expansion and the pull of gravity. The rate of expansion is expressed by the Hubble Constant, Ho, while the strength of gravity depends on the density and pressure of the matter in the universe. If the pressure of the matter is low, as is the case with most forms of matter we know of, then the fate of the universe is governed by the density. If the density of the universe is less than the "critical density" which is proportional to the square of the Hubble constant, then the universe will expand forever. If the density of the universe is greater than the "critical density", then gravity will eventually win and the universe will collapse back on itself, the so called "Big Crunch". However, the results of the WMAP mission and observations of distant supernova have suggested that the expansion of the universe is actually accelerating which implies the existence of a form of matter with a strong negative pressure, such as the cosmological constant. This strange form of matter is also sometimes referred to as "dark energy". If dark energy in fact plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever. http://www.youtube.com/watch?v=kV3 3t8U6w28&feature=related

11. The video of the shape of the universe http://www.youtube.com/watch?v=b3lp0r LtcMM http://www.youtube.com/watch?v=b3lp0r LtcMM http://www.youtube.com/watch?v=b3lp0r LtcMM http://www.youtube.com/watch?v=b3lp0r LtcMM http://www.youtube.com/watch?v=9dpqFsIl1dA&fe ature=related