astronomy - How is the shape of the universe measured by scientists?

I would like to learn how scientists go about measuring the large-scale curvature of the universe to determine if the universe is closed 'i.e. spherical', flat, or open 'i.e. saddle shaped'.

My simplistic thought is that you could measure the corner angles of a really large triangle and see if they add up to <180, 180, or >180 degrees. However I can't imagine how you would do that in practice, (not without owning a Ningi anyway).

Ref. Hitchhiker's Guide to the Galaxy: The 'Triganic Pu' is a Monetary unit. Its exchange rate of eight Ningis to one Pu is simple enough, but since a Ningi is a triangular rubber coin six thousand eight hundred miles along each side, no one has ever collected enough to own one Pu. Ningis are not negotiable currency, because the Galactibanks refuse to deal in fiddling small change.

Answer

There's an excellent talk by Lawrence Krauss on precisely this subject. I can't recommend watching it highly enough, you should start watching it before even reading the remainder of this post.

In summary, we can model the matter just after the big bang at the time we see the cosmic microwave background and determine the characteristic distance scales of the "lumpiness" of the Universe at that point. We can view the lumpiness of the Universe then by observing the cosmic microwave background radiation at high resolution. Now we have something that we can compare the expected visual size of to the apparent visual size, giving us information about the shape of the Universe in between.