6.6 Rotation Symmetry
Brinkman
Geometry
1. Define what a rotation is again! The turning of an object around a point!
2. Apply! Which of the following figures can you rotate, and still get the same figure?
Yes
Yes
Yes
NO
Yes
Yes
2. Define Rotation Symmetry: A figure is a rotation symmetric figure if and only if there is
a rotation R with a magnitude between 00 and 360o such that R(figure) = figure. The center of the
rotation R is called the center point of rotation for the figure.
3. Use the figure below to answer the questions!
a.) How many times does the figure need to be rotated to get back to
the original position? 4 times!
b.) Therefore it has a 4 - FOLD rotation of symmetry because
it takes 4 Rotations of magnitude 90o to get
the figure back to the original position.
Need
To
Know!
4. In general, if m is the smallest positive magnitude for a rotation and
360
if 𝑛 = 𝑚 , then n rotations will bring it back to the original position.
5. Define n-fold rotation symmetry: The NUMBER n of rotations with MAGNITUDE m,
that bring the figure back to the original position.
6. Apply! Look at the following figures. Describe the n-fold symmetry and magnitude.
N – fold: 3 – Fold
Magnitude: 120
N – fold: 5 - Fold
N – fold: 24 - Fold
Magnitude: 72
Magnitude: 15
7. Recall, what is reflection symmetric? The same thing (figure) on both sides of a line of symmetry.
8. Describe whether the figures below are rotation-symmetric and/or/neither reflection-symmetric. Use the
line in each diagram as the line of symmetry.
Rot. Sym? YES
Rot. Sym? YES
Rot. Sym? YES
Rot. Sym? NO
Ref. Sym? NO
Ref. Sym? YES
Ref. Sym? NO
Ref. Sym? YES
N-fold? 2 FOLD
N-fold? 6-FOLD
N-fold? 5 - FOLD
N-fold? 1 - FOLD
Rot. Sym? YES
Rot. Sym? YES
Rot. Sym? NO
Rot. Sym? YES
Ref. Sym? NO
Ref. Sym? YES
Ref. Sym? YES
Ref. Sym? NO
N-fold? 4 - FOLD
N-fold? 2 – FOLD
N-fold? 2 - FOLD
N-fold? 2 FOLD