cuti3panda Posted September 4, 2004 Share Posted September 4, 2004 Bottle caps that are pried off typically have 22 ridges around the rim. Find the symmetry group of such a cap. Please help me this problem, thanks a lot! Link to comment Share on other sites More sharing options...
bloodhound Posted September 5, 2004 Share Posted September 5, 2004 i am not sure of this. havent done this for a while. but most likely you will have 22 rotational symmetries and 22 reflective symmetries. i am not going to list them all but here are some rotational (1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22) (1 3 5 7 9 11 13 15 17 19 21)(2 4 6 8 10 12 14 16 18 20) Link to comment Share on other sites More sharing options...
matt grime Posted September 5, 2004 Share Posted September 5, 2004 In what form are you used to seeing groups presented? From the question it just asks you what the symmetry group of a 22-gon is, which is either D(11) or D(22) depending on the standards in the course you're using. But how do *you* describe groups? There are many ways of doing it, which do you understand? Bloodhounds description for instance amounts to labelling the corners, and the thing in bracket tells you what to do to each corner, the first is the symmetry sending the corner labelled 1 to that labelled 2, that labelled 2 to 3 and so on reading left to right. This, sorry to say, bloodhound, is about the worst way of writing it since it contains so much redundant information: pick three adjacent corners, once you've said where to map them to the symmetry is fixed otherwise yo'ud have to break the cap. So there are 19 numbers in there that do nothing. The best way, perhaps is in terms of generators and relations. Link to comment Share on other sites More sharing options...
cuti3panda Posted September 7, 2004 Author Share Posted September 7, 2004 Matt Grime, would you plz give me more detail about the problem above! it's due on thursday, help me plz....thanks a lot Link to comment Share on other sites More sharing options...
matt grime Posted September 8, 2004 Share Posted September 8, 2004 Any basic group theory book will explain what dihedral groups are. Link to comment Share on other sites More sharing options...
cuti3panda Posted September 8, 2004 Author Share Posted September 8, 2004 thanks again, matt grime! Link to comment Share on other sites More sharing options...
Guest John Doe Posted September 10, 2004 Share Posted September 10, 2004 Please bare with me I need help with a question : Why can't a set be defined Link to comment Share on other sites More sharing options...
Guest John Doe Posted September 10, 2004 Share Posted September 10, 2004 What does mathematics has to say about the term "definition".These are some question ask by my professer Link to comment Share on other sites More sharing options...
bloodhound Posted September 11, 2004 Share Posted September 11, 2004 This' date=' sorry to say, bloodhound, is about the worst way of writing it since it contains so much redundant information: .[/quote'] Hehe , I DID say i havent done this for a while. Link to comment Share on other sites More sharing options...
matt grime Posted September 11, 2004 Share Posted September 11, 2004 Please bare with me I need help with a question : Why can't a set be defined A set can be "defined", it just isn't defined how people first think it is defined. It is not a collection of objects with some rule for belonging. How it should be done is messy and unilluminating at this stage in your development, since the *naive* definition is sufficient for many purposes. As for "definition", that is philosophical, my preferred way is to think of the definition of an object as the set of rules that define its use. Link to comment Share on other sites More sharing options...
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