Exploring Frieze Patterns

Clear your picture ("esborra") and move the Friso slider so that F_{1 is selected.} Now draw something simple to see what happens. a) Are there any reflection symmetries? b) are there any rotation symmetries? c) Why is this the simplest frieze pattern?

Clear your picture ("esborra") and move the Friso slider so that F₁¹ _{is selected.} Now draw something simple to see what happens. a) Are there any reflection symmetries? If so is it vertical or horizontal? b) are there any rotation symmetries?

Clear your picture and move the Friso slider so that F₁² is selected. This Frieze pattern has one kind of reflection symmetry. Make some drawings to determine if it is a horizontal or vertical reflection. Which is it?

Clear your picture ("esborra") and move the Friso slider so that F2¹ _{is selected.} Now draw something simple to see what happens. a) Is there are vertical reflection? b) Is there horizontal reflection? c) are there any rotation symmetries?

One of the frieze pattern types has what's called "glide reflection." This means if you draw a picture of a right foot then the pattern will look like alternating right and left feet walking. can you figure out which frieze pattern has glide reflection?

Can you figure out which symbol in the video (F1, F2, F3... F7) correspond to which symbols in this applet (F_1,F₂, F₁¹ etc) ?

The drawing program we used here has instructions in Catalan, which is spoken in the Barcelona region of Spain. Barcelona is known for art and architecture. Google some pictures and see if you can identify any Frieze patterns.

Many Polynesian and Hawaiian Tattoos include frieze patterns. For the one shown above can you determine what kinds of symmetries it has? can you tell if its F₁, F₂, F₁² etc??