Its a little bit difficult to comprehend the meaning of "the universe is flat". Suppose that we lived in the center of the Earth but we could see the surface of the Earth as well - Suppose that the whole Earth was made out of clear glass. The space between us (in the center) and the surface could be either flat, positively curved (like the surface of a ball) or negatively curved (like the inner surface of the a bottle. Logic dictates that the space between us and the Earth has to be flat, it makes no sense of a curved space, right?
Well, Earth is too small compared to the Universe and it the space between its center and its surface appears to be flat, but this does not mean that the whole universe is flat - Which does not really makes any sense, but yet again, what makes sense in the universe?
So we figured out a way to determine if the space is flat or not. To our glass-made Earth example, suppose that we were able to measure the length of the triangle performed by the center (us) and two points on the surface. With simple (really simple) geometry we can therefore determine if these measurements belongs to a Euclidean triangle or not, by calculating its angles. And this is precisely what we've done to find out if the universe is flat, using the all-sky map of the Cosmic Microwave Background Radiation (CMBR).
There are some randomly placed spots in the CMBR caused by tiny fluctuations in temperature from sound-waves traveling through ionized gas at a known speed. These sports have a known apparent angle of about 1 degree. We also know the distance of these spots from Earth since we know the length of time that these sound waves have been traveling. We then applied trigonometry and found out that the Universe is flat!
Atleast wherever the planets and galaxies are rotating around a central point the space has to be curved according to Einstein,because it is the circular space along with the gravitational attraction that keeps their path circular or elliptical.What about spaces in between?Will space travel become easier with an hyperbolic space?the distance between two points are short here.So universe may not be a flat sheet.It must be of different shape.