### curvature

(unflatness of space)

**Curvature** of space (i.e., a **curved space**) is space
that deviates from the well-known rules of geometry.
Curved spaces can be consistently described mathematically,
and general relativity imagines the space of the universe as non-flat,
to help describe gravity, and cosmological theories
assume some curvature. In both cases, the curvature
is too small to show up in day-to-day measurements.

A curvature of space can be detected by testing
the known rules of flat geometry, in an analogous
manner to how one might measure the curvature of
the Earth's surface through measurement: for example,
laying out a large triangle on the surface consisting
of a given Earth altitude (e.g., sea level) will yield
a shape whose angles do not add up to 180°
or laying out a circle and measuring the ratio
of its circumference and diameter will not yield π.
Precisely these same tests can, in principle,
be done in space, and given enough curvature
and large enough shapes, the curvature could
be measured.

A curvature of space can be positive (analogous to the surface of
a sphere) or negative (analogous to the surface of a saddle shape,
or the inner edge of a doughnut). Sensitive trials have been carried
out to see if any curvature is detectable.

(*cosmology,mathematics,geometry*)
http://en.wikipedia.org/wiki/Curved_space

**Referenced by:**

general relativity (GR)

gravitational wave (GW)

inflation

Lambda-CDM model (ΛCDM)

luminosity distance (d_{L})

radio source counts

redshift-angular size relation

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