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Additional
first fundamental form
English Wikipedia - The Free Encyclopedia
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First fundamental form
In
differential geometry
, the
first fundamental form
is the
inner product
on the
tangent space
of a
surface
in three-dimensional
Euclidean space
which is induced
canonically
from the
dot product
of
R
3
. It permits the calculation of
curvature
and metric properties of a surface such as length and area in a manner consistent with the
ambient space
. The first fundamental form is denoted by the Roman numeral I,
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