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    Is the universe infinite or finite? Or is it so close to infinite that for all practical purposes it is?

    The universe’s geometry determines whether the cosmos is spatially finite or infinite.

    The geometry could be flat, open (meaning negatively curved), or closed (meaning positively curved). In two dimensions, you can represent these geometries by a sheet of paper, the surface of a saddle, and the surface of a ball, respectively.

    In three spatial dimensions, however, they are a bit harder to visualize, but even in 3-D, angles in a triangle sum to 180° in a flat case, less than 180° in the open case, and more than 180° in the closed case.

    The universe is finite if it is positively curved and infinite if it is negatively curved or flat.

    Fortunately, cosmology experiments can measure cosmic geometry.

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  • In particular, the sizes of the hot and cold spots in the cosmic microwave background left over from the early universe are sensitive to the geometry of the universe. The spots appear bigger in positively curved space and smaller in negatively curved space.

    Measurements made over the pa

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