Last Updated
：2025/12/05
real projective plane
Noun
(geometry)
A
three-dimensional
vector
space
over
the
field
of
real
numbers
in
which
one-dimensional
linear
subspaces
are
considered
as
“points”
and
two-dimensional
linear
subspaces
are
considered
as
“lines”.
Equivalently,
a
sphere
in
which
pairs
of
antipodal
points
are
considered
as
“points”
and
great
circles
are
considered
as
“lines”.
Japanese Meaning
実射影平面：実数体上の3次元ベクトル空間において、1次元の線形部分空間を「点」、2次元の線形部分空間を「直線」として扱う幾何学的対象。 / 実射影平面：球面上において、反対称な（対向する）点を1つの点として、また大円を直線として扱う幾何学的構造。
Sense（1）
(geometry)
A
three-dimensional
vector
space
over
the
field
of
real
numbers
in
which
one-dimensional
linear
subspaces
are
considered
as
“points”
and
two-dimensional
linear
subspaces
are
considered
as
“lines”.
Equivalently,
a
sphere
in
which
pairs
of
antipodal
points
are
considered
as
“points”
and
great
circles
are
considered
as
“lines”.
（ plural ）
Quizzes for review
(geometry) A three-dimensional vector space over the field of real numbers in which one-dimensional linear subspaces are considered as “points” and two-dimensional linear subspaces are considered as “lines”. Equivalently, a sphere in which pairs of antipodal points are considered as “points” and great circles are considered as “lines”.
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real projective plane
Topologists often describe the real projective plane as the sphere with antipodal points identified, making it a fundamental example of a nonorientable surface.
See correct answer
Topologists often describe the real projective plane as the sphere with antipodal points identified, making it a fundamental example of a nonorientable surface.
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