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That's an odd coin - I wonder why



The Next CEO of Stack OverflowThe Laziest SurveyorPolyomino Z pentomino and rectangle packing into rectangleCovering Table with CoinsChess at the 2020 Olympic GamesConstructing 0.35 Unit LengthNeed help with a cipherLaser Beams in Helsinki SkiesHow many possible different shapes are there on a 4x4 dot grid?Random chord to a circle around a triangleSpecial triangles in convex polygons










2












$begingroup$


Around the world, there are several roughly polygonal coins. Here's an example:



English Coins



One thing you'll notice is that they all have an odd number of sides. It turns out that this is universally true for modern polygonal coins (if you have an extant example where this is not true, please post it!!)



And it turns out that there's a perfectly sensible reason for this.




Why do modern polygonal coins have an odd number of sides?







geometry real







share|improve this question









$endgroup$











  • $begingroup$
    Have a look here and here
    $endgroup$
    – ielyamani
    3 hours ago
















2












$begingroup$


Around the world, there are several roughly polygonal coins. Here's an example:



English Coins



One thing you'll notice is that they all have an odd number of sides. It turns out that this is universally true for modern polygonal coins (if you have an extant example where this is not true, please post it!!)



And it turns out that there's a perfectly sensible reason for this.




Why do modern polygonal coins have an odd number of sides?







geometry real







share|improve this question









$endgroup$











  • $begingroup$
    Have a look here and here
    $endgroup$
    – ielyamani
    3 hours ago














2












2








2





$begingroup$


Around the world, there are several roughly polygonal coins. Here's an example:



English Coins



One thing you'll notice is that they all have an odd number of sides. It turns out that this is universally true for modern polygonal coins (if you have an extant example where this is not true, please post it!!)



And it turns out that there's a perfectly sensible reason for this.




Why do modern polygonal coins have an odd number of sides?







geometry real







share|improve this question









$endgroup$




Around the world, there are several roughly polygonal coins. Here's an example:



English Coins



One thing you'll notice is that they all have an odd number of sides. It turns out that this is universally true for modern polygonal coins (if you have an extant example where this is not true, please post it!!)



And it turns out that there's a perfectly sensible reason for this.




Why do modern polygonal coins have an odd number of sides?







geometry real




geometry real






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 7 hours ago









Dr XorileDr Xorile

13.9k32977




13.9k32977











  • $begingroup$
    Have a look here and here
    $endgroup$
    – ielyamani
    3 hours ago

















  • $begingroup$
    Have a look here and here
    $endgroup$
    – ielyamani
    3 hours ago
















$begingroup$
Have a look here and here
$endgroup$
– ielyamani
3 hours ago





$begingroup$
Have a look here and here
$endgroup$
– ielyamani
3 hours ago











3 Answers
3






active

oldest

votes


















5












$begingroup$

I'm not entirely sure this is exactly a puzzle (but also not sure enough to suggest closing the question or anything). Anyway, I guess the reason is that




it's useful for them to be shapes of constant width (so that, e.g., they can go nicely into machines that accept coins for payment), and there's a nice simple construction for those that gives you a regular-polygon-ish shape with any odd number of sides; but nothing of that sort can possibly work for an even number of sides (because the diameter would have to be larger "between corners" than "in the middle of the side").







share|improve this answer









$endgroup$




















    5












    $begingroup$

    Looking at this:




    CoinBrothers




    it is rarely true.



    For example, Australia 2019:




    https://coin-brothers.com/catalog/coin3771







    share|improve this answer











    $endgroup$












    • $begingroup$
      @DrXorile; there's more recent later on
      $endgroup$
      – JonMark Perry
      6 hours ago


















    4












    $begingroup$

    The coins have




    A constant diameter.

    No matter how the coin is oriented, the diameter is the same.


    The coins shown have curved edges.

    The centre of the arc which forms the curve, is the opposite point.


    This can't be done with an even number of sides.


    enter image description here




    Note: sadly this was scooped earlier by @Gareth McCaughan.






    share|improve this answer











    $endgroup$












    • $begingroup$
      This says the same thing as my answer posted 40 minutes earlier.
      $endgroup$
      – Gareth McCaughan♦
      3 hours ago










    • $begingroup$
      @GarethMcCaughan, almost. I had already realised it for myself, and it includes information about radii. The time was taken trying to either make a graphic but finally a photograph.
      $endgroup$
      – Weather Vane
      2 hours ago











    • $begingroup$
      For the avoidance of doubt, I'm not accusing you of copying my answer. Only of posting yours without checking whether you'd been scooped. Which, in this case, you had by a considerable margin.
      $endgroup$
      – Gareth McCaughan♦
      2 hours ago










    • $begingroup$
      @GarethMcCaughan as you feel so badly about it, I've given you an upvote. On many Stack Exchange sites, duplicate answers are posted with differents angles. Others take valid comments and turn them into answers. Perhaps it was me who felt "scooped" because I didn't prepare my answer fast enough.
      $endgroup$
      – Weather Vane
      2 hours ago












    Your Answer





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    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    5












    $begingroup$

    I'm not entirely sure this is exactly a puzzle (but also not sure enough to suggest closing the question or anything). Anyway, I guess the reason is that




    it's useful for them to be shapes of constant width (so that, e.g., they can go nicely into machines that accept coins for payment), and there's a nice simple construction for those that gives you a regular-polygon-ish shape with any odd number of sides; but nothing of that sort can possibly work for an even number of sides (because the diameter would have to be larger "between corners" than "in the middle of the side").







    share|improve this answer









    $endgroup$

















      5












      $begingroup$

      I'm not entirely sure this is exactly a puzzle (but also not sure enough to suggest closing the question or anything). Anyway, I guess the reason is that




      it's useful for them to be shapes of constant width (so that, e.g., they can go nicely into machines that accept coins for payment), and there's a nice simple construction for those that gives you a regular-polygon-ish shape with any odd number of sides; but nothing of that sort can possibly work for an even number of sides (because the diameter would have to be larger "between corners" than "in the middle of the side").







      share|improve this answer









      $endgroup$















        5












        5








        5





        $begingroup$

        I'm not entirely sure this is exactly a puzzle (but also not sure enough to suggest closing the question or anything). Anyway, I guess the reason is that




        it's useful for them to be shapes of constant width (so that, e.g., they can go nicely into machines that accept coins for payment), and there's a nice simple construction for those that gives you a regular-polygon-ish shape with any odd number of sides; but nothing of that sort can possibly work for an even number of sides (because the diameter would have to be larger "between corners" than "in the middle of the side").







        share|improve this answer









        $endgroup$



        I'm not entirely sure this is exactly a puzzle (but also not sure enough to suggest closing the question or anything). Anyway, I guess the reason is that




        it's useful for them to be shapes of constant width (so that, e.g., they can go nicely into machines that accept coins for payment), and there's a nice simple construction for those that gives you a regular-polygon-ish shape with any odd number of sides; but nothing of that sort can possibly work for an even number of sides (because the diameter would have to be larger "between corners" than "in the middle of the side").








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 7 hours ago









        Gareth McCaughan♦Gareth McCaughan

        66k3166258




        66k3166258





















            5












            $begingroup$

            Looking at this:




            CoinBrothers




            it is rarely true.



            For example, Australia 2019:




            https://coin-brothers.com/catalog/coin3771







            share|improve this answer











            $endgroup$












            • $begingroup$
              @DrXorile; there's more recent later on
              $endgroup$
              – JonMark Perry
              6 hours ago















            5












            $begingroup$

            Looking at this:




            CoinBrothers




            it is rarely true.



            For example, Australia 2019:




            https://coin-brothers.com/catalog/coin3771







            share|improve this answer











            $endgroup$












            • $begingroup$
              @DrXorile; there's more recent later on
              $endgroup$
              – JonMark Perry
              6 hours ago













            5












            5








            5





            $begingroup$

            Looking at this:




            CoinBrothers




            it is rarely true.



            For example, Australia 2019:




            https://coin-brothers.com/catalog/coin3771







            share|improve this answer











            $endgroup$



            Looking at this:




            CoinBrothers




            it is rarely true.



            For example, Australia 2019:




            https://coin-brothers.com/catalog/coin3771








            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited 6 hours ago

























            answered 7 hours ago









            JonMark PerryJonMark Perry

            20.6k64099




            20.6k64099











            • $begingroup$
              @DrXorile; there's more recent later on
              $endgroup$
              – JonMark Perry
              6 hours ago
















            • $begingroup$
              @DrXorile; there's more recent later on
              $endgroup$
              – JonMark Perry
              6 hours ago















            $begingroup$
            @DrXorile; there's more recent later on
            $endgroup$
            – JonMark Perry
            6 hours ago




            $begingroup$
            @DrXorile; there's more recent later on
            $endgroup$
            – JonMark Perry
            6 hours ago











            4












            $begingroup$

            The coins have




            A constant diameter.

            No matter how the coin is oriented, the diameter is the same.


            The coins shown have curved edges.

            The centre of the arc which forms the curve, is the opposite point.


            This can't be done with an even number of sides.


            enter image description here




            Note: sadly this was scooped earlier by @Gareth McCaughan.






            share|improve this answer











            $endgroup$












            • $begingroup$
              This says the same thing as my answer posted 40 minutes earlier.
              $endgroup$
              – Gareth McCaughan♦
              3 hours ago










            • $begingroup$
              @GarethMcCaughan, almost. I had already realised it for myself, and it includes information about radii. The time was taken trying to either make a graphic but finally a photograph.
              $endgroup$
              – Weather Vane
              2 hours ago











            • $begingroup$
              For the avoidance of doubt, I'm not accusing you of copying my answer. Only of posting yours without checking whether you'd been scooped. Which, in this case, you had by a considerable margin.
              $endgroup$
              – Gareth McCaughan♦
              2 hours ago










            • $begingroup$
              @GarethMcCaughan as you feel so badly about it, I've given you an upvote. On many Stack Exchange sites, duplicate answers are posted with differents angles. Others take valid comments and turn them into answers. Perhaps it was me who felt "scooped" because I didn't prepare my answer fast enough.
              $endgroup$
              – Weather Vane
              2 hours ago
















            4












            $begingroup$

            The coins have




            A constant diameter.

            No matter how the coin is oriented, the diameter is the same.


            The coins shown have curved edges.

            The centre of the arc which forms the curve, is the opposite point.


            This can't be done with an even number of sides.


            enter image description here




            Note: sadly this was scooped earlier by @Gareth McCaughan.






            share|improve this answer











            $endgroup$












            • $begingroup$
              This says the same thing as my answer posted 40 minutes earlier.
              $endgroup$
              – Gareth McCaughan♦
              3 hours ago










            • $begingroup$
              @GarethMcCaughan, almost. I had already realised it for myself, and it includes information about radii. The time was taken trying to either make a graphic but finally a photograph.
              $endgroup$
              – Weather Vane
              2 hours ago











            • $begingroup$
              For the avoidance of doubt, I'm not accusing you of copying my answer. Only of posting yours without checking whether you'd been scooped. Which, in this case, you had by a considerable margin.
              $endgroup$
              – Gareth McCaughan♦
              2 hours ago










            • $begingroup$
              @GarethMcCaughan as you feel so badly about it, I've given you an upvote. On many Stack Exchange sites, duplicate answers are posted with differents angles. Others take valid comments and turn them into answers. Perhaps it was me who felt "scooped" because I didn't prepare my answer fast enough.
              $endgroup$
              – Weather Vane
              2 hours ago














            4












            4








            4





            $begingroup$

            The coins have




            A constant diameter.

            No matter how the coin is oriented, the diameter is the same.


            The coins shown have curved edges.

            The centre of the arc which forms the curve, is the opposite point.


            This can't be done with an even number of sides.


            enter image description here




            Note: sadly this was scooped earlier by @Gareth McCaughan.






            share|improve this answer











            $endgroup$



            The coins have




            A constant diameter.

            No matter how the coin is oriented, the diameter is the same.


            The coins shown have curved edges.

            The centre of the arc which forms the curve, is the opposite point.


            This can't be done with an even number of sides.


            enter image description here




            Note: sadly this was scooped earlier by @Gareth McCaughan.







            share|improve this answer














            share|improve this answer



            share|improve this answer








            edited 56 mins ago

























            answered 6 hours ago









            Weather VaneWeather Vane

            2,047110




            2,047110











            • $begingroup$
              This says the same thing as my answer posted 40 minutes earlier.
              $endgroup$
              – Gareth McCaughan♦
              3 hours ago










            • $begingroup$
              @GarethMcCaughan, almost. I had already realised it for myself, and it includes information about radii. The time was taken trying to either make a graphic but finally a photograph.
              $endgroup$
              – Weather Vane
              2 hours ago











            • $begingroup$
              For the avoidance of doubt, I'm not accusing you of copying my answer. Only of posting yours without checking whether you'd been scooped. Which, in this case, you had by a considerable margin.
              $endgroup$
              – Gareth McCaughan♦
              2 hours ago










            • $begingroup$
              @GarethMcCaughan as you feel so badly about it, I've given you an upvote. On many Stack Exchange sites, duplicate answers are posted with differents angles. Others take valid comments and turn them into answers. Perhaps it was me who felt "scooped" because I didn't prepare my answer fast enough.
              $endgroup$
              – Weather Vane
              2 hours ago

















            • $begingroup$
              This says the same thing as my answer posted 40 minutes earlier.
              $endgroup$
              – Gareth McCaughan♦
              3 hours ago










            • $begingroup$
              @GarethMcCaughan, almost. I had already realised it for myself, and it includes information about radii. The time was taken trying to either make a graphic but finally a photograph.
              $endgroup$
              – Weather Vane
              2 hours ago











            • $begingroup$
              For the avoidance of doubt, I'm not accusing you of copying my answer. Only of posting yours without checking whether you'd been scooped. Which, in this case, you had by a considerable margin.
              $endgroup$
              – Gareth McCaughan♦
              2 hours ago










            • $begingroup$
              @GarethMcCaughan as you feel so badly about it, I've given you an upvote. On many Stack Exchange sites, duplicate answers are posted with differents angles. Others take valid comments and turn them into answers. Perhaps it was me who felt "scooped" because I didn't prepare my answer fast enough.
              $endgroup$
              – Weather Vane
              2 hours ago
















            $begingroup$
            This says the same thing as my answer posted 40 minutes earlier.
            $endgroup$
            – Gareth McCaughan♦
            3 hours ago




            $begingroup$
            This says the same thing as my answer posted 40 minutes earlier.
            $endgroup$
            – Gareth McCaughan♦
            3 hours ago












            $begingroup$
            @GarethMcCaughan, almost. I had already realised it for myself, and it includes information about radii. The time was taken trying to either make a graphic but finally a photograph.
            $endgroup$
            – Weather Vane
            2 hours ago





            $begingroup$
            @GarethMcCaughan, almost. I had already realised it for myself, and it includes information about radii. The time was taken trying to either make a graphic but finally a photograph.
            $endgroup$
            – Weather Vane
            2 hours ago













            $begingroup$
            For the avoidance of doubt, I'm not accusing you of copying my answer. Only of posting yours without checking whether you'd been scooped. Which, in this case, you had by a considerable margin.
            $endgroup$
            – Gareth McCaughan♦
            2 hours ago




            $begingroup$
            For the avoidance of doubt, I'm not accusing you of copying my answer. Only of posting yours without checking whether you'd been scooped. Which, in this case, you had by a considerable margin.
            $endgroup$
            – Gareth McCaughan♦
            2 hours ago












            $begingroup$
            @GarethMcCaughan as you feel so badly about it, I've given you an upvote. On many Stack Exchange sites, duplicate answers are posted with differents angles. Others take valid comments and turn them into answers. Perhaps it was me who felt "scooped" because I didn't prepare my answer fast enough.
            $endgroup$
            – Weather Vane
            2 hours ago





            $begingroup$
            @GarethMcCaughan as you feel so badly about it, I've given you an upvote. On many Stack Exchange sites, duplicate answers are posted with differents angles. Others take valid comments and turn them into answers. Perhaps it was me who felt "scooped" because I didn't prepare my answer fast enough.
            $endgroup$
            – Weather Vane
            2 hours ago


















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