There are surfaces of positive curvature, like a sphere there are surfaces of negative curvature, like a horseвЂ™s saddle there are surfaces of zero curvature, like a flat sheet of paper. In fact, there are three types of fundamentally different spatial surfaces. The reason is the same reason that you canвЂ™t вЂњpeelвЂќ a sphere and lay it out flat to make a square: the surface of a sphere is fundamentally curved and not flat.

In fact, every line of longitude intersects at two points: the north and south poles. If EuclidвЂ™s fifth postulate were true, then any two lines of longitude could never intersect.Д«ut lines of longitude do intersect. Since the equator is a straight line, and all the lines of longitude are straight lines, this tells us that - at least at the equator - the lines of longitude are parallel. Why is this? ThatвЂ™s what Stan Echols wants to know, writing in to ask:Д®very line of longitude you can draw makes a complete circle around the Earth, crossing the equator and making a 90В° angle wherever it does. Yet somehow, when it comes to the Universe as a whole, space itself appears indistinguishable from perfectly flat. But weвЂ™ve come a long way in our understanding since then, and not only can space itself be curved by the presence of matter and energy, but we can witness those effects. Then you would have applied NewtonвЂ™s laws of physics and presumed that things like forces between any two objects would act along the one and only straight line connecting that. Like everyone else, you would have learned geometry starting from the rules of Euclid, where space is nothing more than a three-dimensional grid. What is the shape of the Universe? If you had come along before the 1800s, it likely never would have occurred to you that the Universe itself could even have a shape. ESO and deviantART user InTheStarlightGarden The Universe could also be closed and positively curved: like a hypersphere. location, even in an uncurved (flat) spacetime. In a hypertorus model of the Universe, motion in a straight line will return you to your original.

Negatively curved space