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Rotationslinien

Rotationslinien is a term found in some German-language mathematical writings, but it is not a standard term across modern textbooks. It is used informally to refer to lines that are related to a rotation operation, typically within discussions of symmetry or rotation groups.

In planar geometry, consider a rotation R about a fixed center O by an angle θ. One can

In three dimensions, some authors use the term to denote the axis of rotation or a line

Applications and notes:

- The concept appears in discussions of symmetry, group actions, and the study of how lines transform

See also: Rotationsachse; Orbit; Group action; Symmetry.

study
the
orbit
of
a
geometric
object
under
the
cyclic
group
generated
by
R.
The
Rotationslinie
of
a
line
L
(or
of
a
point
X)
can
then
be
interpreted
as
the
set
of
all
images
under
the
powers
of
R:
{R^k(L)}
or
{R^k(X)}.
If
θ
is
a
rational
multiple
of
π,
this
orbit
is
finite;
if
θ
is
irrational,
the
orbit
is
infinite
and
can
be
dense
in
the
relevant
region.
The
idea
emphasizes
the
lineage
of
positions
a
line
or
point
assumes
under
repeated
rotations.
that
participates
in
a
family
of
rotated
positions
within
a
configuration.
However,
the
standard,
widely
accepted
terms
are
Rotationsachse
(axis
of
rotation)
or
the
more
general
notion
of
a
line
involved
in
a
symmetry
operation;
Rotationslinie
is
less
formal
and
not
commonly
used
in
rigorous
treatments.
under
repeated
rotations
in
geometry
or
computer
graphics.