Group theory, dihedral group












2












$begingroup$


Why we study dihedral group? Please tell Real life example of dihedral group. I know this group mathematically.




From the comments: Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.






abstract-algebra







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$endgroup$












  • $begingroup$
    This question is unclear and somewhat unmotivated. What do you mean be a real life example? If you want somebody to point at a structure in the universe with dihedral symmetry that is easy, but easily too broad. Would you like such an answer? We have had quality threads about "real life" applications of group theory. Would those help you?
    $endgroup$
    – Jyrki Lahtonen
    Nov 23 '15 at 9:20












  • $begingroup$
    Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.
    $endgroup$
    – user270371
    Nov 23 '15 at 9:25










  • $begingroup$
    One possibly related thread and another. Not really specific to dihedral groups. But thanks for the comment. It does clarify your needs.
    $endgroup$
    – Jyrki Lahtonen
    Nov 23 '15 at 9:45








  • 2




    $begingroup$
    It makes no sense to tell your friends about the meaning of the dihedral group before telling them about groups and symmetries in general (see Jyrki's links). Perhaps this has nothing to do with your friends, but just to understand more about dihedral groups. If so, you should pose a question, which is more detailed.
    $endgroup$
    – Dietrich Burde
    Nov 23 '15 at 10:24












  • $begingroup$
    When I've googled dihedral group, uses I've find for example maa.org/sites/default/files/images/upload_library/4/vol1/… where is cited that the group is used in the classification of molecules and crystals, too to made designs.I'm agree with Burde's comment.
    $endgroup$
    – user243301
    Nov 23 '15 at 10:33


















2












$begingroup$


Why we study dihedral group? Please tell Real life example of dihedral group. I know this group mathematically.




From the comments: Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.






abstract-algebra







share|cite|improve this question











$endgroup$












  • $begingroup$
    This question is unclear and somewhat unmotivated. What do you mean be a real life example? If you want somebody to point at a structure in the universe with dihedral symmetry that is easy, but easily too broad. Would you like such an answer? We have had quality threads about "real life" applications of group theory. Would those help you?
    $endgroup$
    – Jyrki Lahtonen
    Nov 23 '15 at 9:20












  • $begingroup$
    Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.
    $endgroup$
    – user270371
    Nov 23 '15 at 9:25










  • $begingroup$
    One possibly related thread and another. Not really specific to dihedral groups. But thanks for the comment. It does clarify your needs.
    $endgroup$
    – Jyrki Lahtonen
    Nov 23 '15 at 9:45








  • 2




    $begingroup$
    It makes no sense to tell your friends about the meaning of the dihedral group before telling them about groups and symmetries in general (see Jyrki's links). Perhaps this has nothing to do with your friends, but just to understand more about dihedral groups. If so, you should pose a question, which is more detailed.
    $endgroup$
    – Dietrich Burde
    Nov 23 '15 at 10:24












  • $begingroup$
    When I've googled dihedral group, uses I've find for example maa.org/sites/default/files/images/upload_library/4/vol1/… where is cited that the group is used in the classification of molecules and crystals, too to made designs.I'm agree with Burde's comment.
    $endgroup$
    – user243301
    Nov 23 '15 at 10:33
















2












2








2


1



$begingroup$


Why we study dihedral group? Please tell Real life example of dihedral group. I know this group mathematically.




From the comments: Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.






abstract-algebra







share|cite|improve this question











$endgroup$




Why we study dihedral group? Please tell Real life example of dihedral group. I know this group mathematically.




From the comments: Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.






abstract-algebra




abstract-algebra






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Dec 29 '18 at 11:49









Shaun

10.6k113687




10.6k113687










asked Nov 23 '15 at 9:14









user270371user270371

193




193












  • $begingroup$
    This question is unclear and somewhat unmotivated. What do you mean be a real life example? If you want somebody to point at a structure in the universe with dihedral symmetry that is easy, but easily too broad. Would you like such an answer? We have had quality threads about "real life" applications of group theory. Would those help you?
    $endgroup$
    – Jyrki Lahtonen
    Nov 23 '15 at 9:20












  • $begingroup$
    Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.
    $endgroup$
    – user270371
    Nov 23 '15 at 9:25










  • $begingroup$
    One possibly related thread and another. Not really specific to dihedral groups. But thanks for the comment. It does clarify your needs.
    $endgroup$
    – Jyrki Lahtonen
    Nov 23 '15 at 9:45








  • 2




    $begingroup$
    It makes no sense to tell your friends about the meaning of the dihedral group before telling them about groups and symmetries in general (see Jyrki's links). Perhaps this has nothing to do with your friends, but just to understand more about dihedral groups. If so, you should pose a question, which is more detailed.
    $endgroup$
    – Dietrich Burde
    Nov 23 '15 at 10:24












  • $begingroup$
    When I've googled dihedral group, uses I've find for example maa.org/sites/default/files/images/upload_library/4/vol1/… where is cited that the group is used in the classification of molecules and crystals, too to made designs.I'm agree with Burde's comment.
    $endgroup$
    – user243301
    Nov 23 '15 at 10:33




















  • $begingroup$
    This question is unclear and somewhat unmotivated. What do you mean be a real life example? If you want somebody to point at a structure in the universe with dihedral symmetry that is easy, but easily too broad. Would you like such an answer? We have had quality threads about "real life" applications of group theory. Would those help you?
    $endgroup$
    – Jyrki Lahtonen
    Nov 23 '15 at 9:20












  • $begingroup$
    Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.
    $endgroup$
    – user270371
    Nov 23 '15 at 9:25










  • $begingroup$
    One possibly related thread and another. Not really specific to dihedral groups. But thanks for the comment. It does clarify your needs.
    $endgroup$
    – Jyrki Lahtonen
    Nov 23 '15 at 9:45








  • 2




    $begingroup$
    It makes no sense to tell your friends about the meaning of the dihedral group before telling them about groups and symmetries in general (see Jyrki's links). Perhaps this has nothing to do with your friends, but just to understand more about dihedral groups. If so, you should pose a question, which is more detailed.
    $endgroup$
    – Dietrich Burde
    Nov 23 '15 at 10:24












  • $begingroup$
    When I've googled dihedral group, uses I've find for example maa.org/sites/default/files/images/upload_library/4/vol1/… where is cited that the group is used in the classification of molecules and crystals, too to made designs.I'm agree with Burde's comment.
    $endgroup$
    – user243301
    Nov 23 '15 at 10:33


















$begingroup$
This question is unclear and somewhat unmotivated. What do you mean be a real life example? If you want somebody to point at a structure in the universe with dihedral symmetry that is easy, but easily too broad. Would you like such an answer? We have had quality threads about "real life" applications of group theory. Would those help you?
$endgroup$
– Jyrki Lahtonen
Nov 23 '15 at 9:20






$begingroup$
This question is unclear and somewhat unmotivated. What do you mean be a real life example? If you want somebody to point at a structure in the universe with dihedral symmetry that is easy, but easily too broad. Would you like such an answer? We have had quality threads about "real life" applications of group theory. Would those help you?
$endgroup$
– Jyrki Lahtonen
Nov 23 '15 at 9:20














$begingroup$
Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.
$endgroup$
– user270371
Nov 23 '15 at 9:25




$begingroup$
Actually I am going to tell about dihedral group to friends. So in introduction to dihedral group I have to tell the use of dihedral group in practicle life.why we need dihedral group. From where this originate.
$endgroup$
– user270371
Nov 23 '15 at 9:25












$begingroup$
One possibly related thread and another. Not really specific to dihedral groups. But thanks for the comment. It does clarify your needs.
$endgroup$
– Jyrki Lahtonen
Nov 23 '15 at 9:45






$begingroup$
One possibly related thread and another. Not really specific to dihedral groups. But thanks for the comment. It does clarify your needs.
$endgroup$
– Jyrki Lahtonen
Nov 23 '15 at 9:45






2




2




$begingroup$
It makes no sense to tell your friends about the meaning of the dihedral group before telling them about groups and symmetries in general (see Jyrki's links). Perhaps this has nothing to do with your friends, but just to understand more about dihedral groups. If so, you should pose a question, which is more detailed.
$endgroup$
– Dietrich Burde
Nov 23 '15 at 10:24






$begingroup$
It makes no sense to tell your friends about the meaning of the dihedral group before telling them about groups and symmetries in general (see Jyrki's links). Perhaps this has nothing to do with your friends, but just to understand more about dihedral groups. If so, you should pose a question, which is more detailed.
$endgroup$
– Dietrich Burde
Nov 23 '15 at 10:24














$begingroup$
When I've googled dihedral group, uses I've find for example maa.org/sites/default/files/images/upload_library/4/vol1/… where is cited that the group is used in the classification of molecules and crystals, too to made designs.I'm agree with Burde's comment.
$endgroup$
– user243301
Nov 23 '15 at 10:33






$begingroup$
When I've googled dihedral group, uses I've find for example maa.org/sites/default/files/images/upload_library/4/vol1/… where is cited that the group is used in the classification of molecules and crystals, too to made designs.I'm agree with Burde's comment.
$endgroup$
– user243301
Nov 23 '15 at 10:33












1 Answer
1






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oldest

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5












$begingroup$

The first (as in at an earliest age) example of a dihedral group in action that most of your friends have seen is the kaleidoscope.



There the viewer sees a pattern $P$, its reflected image, the reflection of the reflection et cetera. Altogether the view consists of parts like $g(P)$, where $g$ ranges over a dihedral group. Or a bigger group - all depending on how many mirrors are used (with two mirrors you get the dihedral group).






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    1 Answer
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    active

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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    5












    $begingroup$

    The first (as in at an earliest age) example of a dihedral group in action that most of your friends have seen is the kaleidoscope.



    There the viewer sees a pattern $P$, its reflected image, the reflection of the reflection et cetera. Altogether the view consists of parts like $g(P)$, where $g$ ranges over a dihedral group. Or a bigger group - all depending on how many mirrors are used (with two mirrors you get the dihedral group).






    share|cite|improve this answer









    $endgroup$


















      5












      $begingroup$

      The first (as in at an earliest age) example of a dihedral group in action that most of your friends have seen is the kaleidoscope.



      There the viewer sees a pattern $P$, its reflected image, the reflection of the reflection et cetera. Altogether the view consists of parts like $g(P)$, where $g$ ranges over a dihedral group. Or a bigger group - all depending on how many mirrors are used (with two mirrors you get the dihedral group).






      share|cite|improve this answer









      $endgroup$
















        5












        5








        5





        $begingroup$

        The first (as in at an earliest age) example of a dihedral group in action that most of your friends have seen is the kaleidoscope.



        There the viewer sees a pattern $P$, its reflected image, the reflection of the reflection et cetera. Altogether the view consists of parts like $g(P)$, where $g$ ranges over a dihedral group. Or a bigger group - all depending on how many mirrors are used (with two mirrors you get the dihedral group).






        share|cite|improve this answer









        $endgroup$



        The first (as in at an earliest age) example of a dihedral group in action that most of your friends have seen is the kaleidoscope.



        There the viewer sees a pattern $P$, its reflected image, the reflection of the reflection et cetera. Altogether the view consists of parts like $g(P)$, where $g$ ranges over a dihedral group. Or a bigger group - all depending on how many mirrors are used (with two mirrors you get the dihedral group).







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 23 '15 at 11:00









        Jyrki LahtonenJyrki Lahtonen

        110k13172392




        110k13172392






























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