Frieze Pattern

1
Frieze Pattern

• An arrangement of numbers at the intersection of
  two sets of perpendicular diagonals.
• Consists of repeated translations of a pattern
  along a line.

2
No Other Symmetry
This pattern contains only translation symmetry
and was a design made in Spain.
3
Horizontal Symmetry
This picture is divided by a horizontal line
right through the middle and is the same on each
side.
4
Point Symmetry

• In a point symmetry, the center point is a
  midpoint to every segment formed by joining a
  point to its image
• This figure shows two points and their
  reflections through a point. 

5
Glide-reflection Symmetry

• A Glide reflection combines a reflection with a
  translation along the direction of the mirror
  line. They are the only type of symmetry that
  involves more that on step.

6
Vertical Line Symmetry

• This picture can be divided by a vertical line
  with the same image on each side.

7
Vertical Line and Glide-reflection symmetry

• This one combines both vertical line and glide
  reflection

8
Vertical and Horizontal Line symmetry

• This can be divided by either a vertical or a
  horizontal line and have the same image on each
  side.

9
Wallpaper Pattern

• A plane pattern with translation symmetry along
  more that one line.

10
Translation symmetry

• Every translation has a direction and a distance.
  everything is moved by the same amount and in the
  same direction

11
Rotational Symmetry

• Every rotation has a rotocenter and an angle.
  everything rotates by the same amount around that
  point

12
Line Symmetry

• A reflection fixes a mirror line in the plane and
  exchanges points from one side of the line with
  points on the other side of the mirror at the
  same distance from the mirror.

13
Glide-reflection Symmetry

• A glide reflection is a mirror reflection
  followed by a translation parallel to the mirror.
  A glide reflection has a mirror line and
  translation distance.

14
Work Cited

• http//www.joma.org/Math/wallpattern.html
• http//www.fandm.edu/Departments/Mathematics
• http//www.btinternet.com/connectionsinspace/Patt
  erns_and_Space_Filling/Frieze_Patterns/body_frieze
  _patterns.html