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.

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I highly recommend reading the book "Sphereland" by Dionys Burger. It is a "sequel" to the much older book "Flatland" by Edwin Abbott that discusses this issue from the standpoint of going down a dimension -- so if we lived in 2D, how would we measure curvature of our 2D universe in higher dimensions when we can't experience them. – Stuart Robbins Jul 30 '11 at 5:46
– Ben Crowell Jun 24 '13 at 14:24