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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
$begingroup$
Around the world, there are several roughly polygonal coins. Here's an example:
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
asked 7 hours ago
Dr XorileDr Xorile
13.9k32977
$endgroup$
add a comment |
$begingroup$
Around the world, there are several roughly polygonal coins. Here's an example:
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
asked 7 hours ago
Dr XorileDr Xorile
13.9k32977
$endgroup$
$begingroup$
Have a look here and here
$endgroup$
– ielyamani
3 hours ago
add a comment |
$begingroup$
Around the world, there are several roughly polygonal coins. Here's an example:
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
asked 7 hours ago
Dr XorileDr Xorile
13.9k32977
$endgroup$
Around the world, there are several roughly polygonal coins. Here's an example:
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
asked 7 hours ago
Dr XorileDr Xorile
13.9k32977
asked 7 hours ago
Dr XorileDr Xorile
13.9k32977
asked 7 hours ago
Dr XorileDr Xorile
13.9k32977
asked 7 hours ago
Dr XorileDr Xorile
13.9k32977
asked 7 hours ago
Dr XorileDr Xorile
13.9k32977
13.9k32977
$begingroup$
Have a look here and here
$endgroup$
– ielyamani
3 hours ago
add a comment |
$begingroup$
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
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
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").
answered 7 hours ago
Gareth McCaughan♦Gareth McCaughan
66k3166258
$endgroup$
add a comment |
$begingroup$
Looking at this:
CoinBrothers
it is rarely true.
For example, Australia 2019:
https://coin-brothers.com/catalog/coin3771
answered 7 hours ago
JonMark PerryJonMark Perry
20.6k64099
$endgroup$
$begingroup$
@DrXorile; there's more recent later on
$endgroup$
– JonMark Perry
6 hours ago
add a comment |
$begingroup$
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.
Note: sadly this was scooped earlier by @Gareth McCaughan.
answered 6 hours ago
Weather VaneWeather Vane
2,047110
$endgroup$
$begingroup$
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
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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").
answered 7 hours ago
Gareth McCaughan♦Gareth McCaughan
66k3166258
$endgroup$
add a comment |
$begingroup$
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").
answered 7 hours ago
Gareth McCaughan♦Gareth McCaughan
66k3166258
$endgroup$
add a comment |
$begingroup$
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").
answered 7 hours ago
Gareth McCaughan♦Gareth McCaughan
66k3166258
$endgroup$
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").
answered 7 hours ago
Gareth McCaughan♦Gareth McCaughan
66k3166258
answered 7 hours ago
Gareth McCaughan♦Gareth McCaughan
66k3166258
answered 7 hours ago
Gareth McCaughan♦Gareth McCaughan
66k3166258
answered 7 hours ago
Gareth McCaughan♦Gareth McCaughan
66k3166258
66k3166258
add a comment |
add a comment |
$begingroup$
Looking at this:
CoinBrothers
it is rarely true.
For example, Australia 2019:
https://coin-brothers.com/catalog/coin3771
answered 7 hours ago
JonMark PerryJonMark Perry
20.6k64099
$endgroup$
$begingroup$
@DrXorile; there's more recent later on
$endgroup$
– JonMark Perry
6 hours ago
add a comment |
$begingroup$
Looking at this:
CoinBrothers
it is rarely true.
For example, Australia 2019:
https://coin-brothers.com/catalog/coin3771
answered 7 hours ago
JonMark PerryJonMark Perry
20.6k64099
$endgroup$
$begingroup$
@DrXorile; there's more recent later on
$endgroup$
– JonMark Perry
6 hours ago
add a comment |
$begingroup$
Looking at this:
CoinBrothers
it is rarely true.
For example, Australia 2019:
https://coin-brothers.com/catalog/coin3771
answered 7 hours ago
JonMark PerryJonMark Perry
20.6k64099
$endgroup$
Looking at this:
CoinBrothers
it is rarely true.
For example, Australia 2019:
https://coin-brothers.com/catalog/coin3771
answered 7 hours ago
JonMark PerryJonMark Perry
20.6k64099
edited 6 hours ago
answered 7 hours ago
JonMark PerryJonMark Perry
20.6k64099
answered 7 hours ago
JonMark PerryJonMark Perry
20.6k64099
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
add a comment |
$begingroup$
@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
add a comment |
$begingroup$
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.
Note: sadly this was scooped earlier by @Gareth McCaughan.
answered 6 hours ago
Weather VaneWeather Vane
2,047110
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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.
Note: sadly this was scooped earlier by @Gareth McCaughan.
answered 6 hours ago
Weather VaneWeather Vane
2,047110
$endgroup$
$begingroup$
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
add a comment |
$begingroup$
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.
Note: sadly this was scooped earlier by @Gareth McCaughan.
answered 6 hours ago
Weather VaneWeather Vane
2,047110
$endgroup$
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.
Note: sadly this was scooped earlier by @Gareth McCaughan.
answered 6 hours ago
Weather VaneWeather Vane
2,047110
edited 56 mins ago
answered 6 hours ago
Weather VaneWeather Vane
2,047110
answered 6 hours ago
Weather VaneWeather Vane
2,047110
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
add a comment |
$begingroup$
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
add a comment |
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$begingroup$
Have a look here and here
$endgroup$
– ielyamani
3 hours ago