What is meant by the term “flat universe”? How is this flatness supported by measurements of the cosmic microwave background?

Space is flat if the three angles of any triangle add up to 180°. For example, Earth’s surface is a positively curved two-dimensional space. When you go from the North Pole to Ecuador to Congo and back to the North Pole, you make a triangle whose angles add up to about 270°. All other triangles on this spherical surface also give more than 180°. A saddle-shape surface is negatively curved. Draw a triangle on it, and the angles will sum to less than 180°.

Cosmic microwave background (CMB) researchers using data from the Wilkinson Microwave Anisotropy Probe (WMAP) have measured the angles of the longest triangle you can imagine. One corner is on Earth, and the other two are so far away that light has traveled about 13.3 billion years to reach us. Scientists found the angles of this triangle add up to 180°, to within small measurement uncertainties.

The far edge of this distant triangle corresponds to the size of a typical spot on the CMB map — each splotch has an angular size similar to the Moon’s. The spots are hot and cold areas in the hydrogen plasma that filled the infant universe, and have been imaged with sensitive microwave cameras aboard WMAP. — MAX TEGMARK, MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE