Exploring Frieze Patterns
[color=#b20ea8][b]Make a pattern by dragging the blue dot. [br][/b][/color]To put the dot back in the center click "centra punter"[br]To erase all click "esborra" [br]The slider "friso" selects different kinds of Frieze symmetry patterns (these have names like F[sub]2[/sub][sup]2[/sup])[br]First just play around using different Frieze patterns and notice that the kinds of symmetries change for the different "frisos"
1.
Clear your picture ("esborra") and move the Friso slider so that F[sub]1 is selected.[br][/sub]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?
2.
Clear your picture ("esborra") and move the Friso slider so that F[sub]1[/sub][sup]1[/sup][sub] is selected.[br][/sub]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?
3.
Clear your picture and move the Friso slider so that F[sub]1[/sub][sup]2 [/sup]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?
4
Clear your picture ("esborra") and move the Friso slider so that F2[sup]1[/sup][sub] is selected.[br][/sub]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?
5.
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?
Here's a great video on frieze patterns.
Its important to note that in this video the symbols used for the 7 patterns are different than we've used above. [br][br]https://youtu.be/524gLKdaMZM[br][url=https://youtu.be/524gLKdaMZM][br]video[/url]
6.
Can you figure out which symbol in the video (F1, F2, F3... F7) correspond to which symbols in this applet (F[sub]1,[/sub]F[sub]2[/sub], F[sub]1[/sub][sup]1 [/sup] etc) [sub] [/sub]?
7.
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 F[sub]1[/sub], F[sub]2[/sub], F[sub]1[/sub][sup]2 [/sup]etc??
Anata Tattoo