Question

How do I do this problem? It's about transformations of frieze patterns.

Answer 1

I could really use some help please.

Answer 2

What kinds of transformations do you know about?

Answer 3

I kinda know the basics like reflections and stuff, but not much more than that. The last time was taught this stuff was in like 6th grade.

Answer 4

That seems pretty sufficient to answer this question actually. Just go down the list of possible transformations and try them out in your mind on each pattern.

Tell me all the translations you think they have and I'll help you make sure you get them all.

Answer 5

For #5 it seems like it can only be flipped.

Answer 6

I'd be more specific and say that it can reflect across the y-axis and also be translated. Although I don't know if you're considering translations as a transformation or not.

Answer 7

For instance, 8 can be reflected across the x-axis, which is a different kind of reflection than 5 has.

Answer 8

Ok, I see what you mean. Also, if translations are counted as transformations, does that mean all of them can be translated.

Answer 9

If you want to leave while I type what I think all the transformations are, you can. I'll tag you when I'm finished if it's ok with you.

Answer 10

Yeah, that's fine. They're all able to be translated, I think that's sort of a fundamental property of frieze patterns but I really don't know that much about them other than I've heard them and they come up often.

Answer 11

It just seems like I'm here but I really have multiple tabs open at once lol.

Answer 12

#5: Translation, rotated 360 degrees, and reflected over the y-axis
#6: Translation, rotated 360 degrees, and reflected over the y-axis
#7: Rotated 360 degrees
#8: Translation, rotated 360 degrees, and reflected over the x-axis
#9: Translation, rotated 360 degrees, and reflected over the x-axis
#10: Translation

@Kainui

Answer 13

6 can be rotated 180 degrees, and also reflected across the x-axis and then translated slightly.

7 can be rotated 180 degrees as well and also be translated

10 also has much more than just translation going for it, see if you can find them.

Everything has at the very least translation and 360 degree rotation.

I think that's all of them otherwise, good job. =)

Answer 14

Ok, I'll check #10 again.

For #10, I only see the 360 degrees rotation along with the translation. Is there anything else that I'm missing?

Answer 15

@Kainui

Answer 16

It should have all the same transformations that 6 has.