8 ms·

How to arrange any number of stars on the U.S. flag (2016)

55 points by jbm 4y ago

082349872349872 4y ago
> I limited the iterations to values of w between h and 5h (which still allows for really too oblong arrangements for higher values...) and listed only totals up to 200 stars, allowing for really aggressive Manifest Destiny scenarios and/or Balkanization within the current borders. Unfortunately if we tried to achieve senatorial parity by giving all states an equivalent population to Wyoming, ~664 states would be necessary. Fortunately the author gives recurrence relations, so even unlisted numbers of stars are, as per the title, arrangeable.
- Mountain_Skies 4y ago
  Plus the name of the country would need to be changed to the United Electoral Districts.
w-m 4y ago
Here's an advent of code puzzle for ya: build a page with four giant renders of the flag (q⃰, e⃰, p⃰ and r⃰), live updated by a slider that goes from 1 to 200. If there's multiple solutions for a certain pattern given a number of stars, choose the one that leaves the least amount of empty space around the stars. :)
Javantea_ 4y ago
This helps answer a serious argument I had on whether Puerto Rico and/or Washington D.C. should become states. Some people argued that the the flag could stay the same. I think the most clever answer would be to make a flag with a star randomly placed to annoy flag-obsessed nerds. More seriously, I think the reason that a 51st or 52nd state can't be added is that the urgency of the matter is lacking. Doing something about statehood would require it to be exceedingly popular and even then the odds are poor.
- cratermoon 4y ago
  > think the reason that a 51st or 52nd state can't be added is that the urgency of the matter is lacking. The reason for the resistance to statehood for Puerto Rico and D.C. is because they both lean heavily Democratic, and the prospect of 2 or 4 more Democratic Senators is unacceptable to the Republicans.
  - friend_and_foe 4y ago
    I don't think that's the entirety of it. DC becoming a state is significantly more problematic than just the politics of it's residents, it's potentially unconstitutional. It makes more sense to cede the city outside the capitol to Maryland and Virginia and allow for representation that way (and what IMO should've been done instead of giving DC 3 electoral college votes via a constitutional amendment), and an amendment to make DC a state would require a lot of reorganizing, the clause providing for a 10 by 10 square mile federal district, the reasoning that the sovereignty of the united states can't be under jurisdiction of a state, it's just messy. Puerto Rico, I think the political balance between parties is largely the prohibiting factor, you're right. But there are other issues, they are not compliant on a lot of requirements for statehood as per US law (congress has the power to regulate this with any legislation), and it seems the status quo in Puerto Rico is exactly what the more powerful political and financial interests there want.
    - cratermoon 4y ago
      > they are not compliant on a lot of requirements for statehood as per US law (congress has the power to regulate this with any legislation) Hmm, I wonder how those laws got to be that way. It's a mystery.
      - friend_and_foe 4y ago
        Say what you mean. Puerto Rico has blatantly unconstitutional gun laws. It has a minimum wage under the federal minimum wage. The US congress requires all applicant territories for statehood have constitutions compliant with the US constitution (a problem for North Dakhota until 1997 funny enough), have laws requiring child support on the books and a whole host of other laws. Puerto Rico is compliant on some fronts and not on others.
friend_and_foe 4y ago
A lot of people don't know this, but there's actually no laws or rules about how you have to arrange stars on the flag, other than that they have to be white on a blue field. You can have a flag with one big star in the middle and 49 tiny stars around it, and it is valid as the US flag, you can have a mess of them, they can be upside down or sideways. I don't just mean the government can decide, I mean that you can make a flag like this and fly it and it is the US flag. Convention dictates though that all stars be of the same size, symbolism for the states all being equally co-sovereign over the union, and the arrangement revealed after a new state joins the union is usually what gets manufactured and becomes the not so official "official" flag.
- chrisshroba 4y ago
  I believe you, but do you have a source so I can read more?
  - macintux 4y ago
    Not the OP, but this looks like the definitive resource. Still skimming it myself out of curiosity. https://www.govinfo.gov/content/pkg/USCODE-2011-title4/pdf/USCODE-2011-title4-chap1.pdf https://www.govinfo.gov/content/pkg/USCODE-2011-title4/pdf/U...
    - deleted 4y ago
      [deleted]
    - pinkmuffinere 4y ago
      Thanks for finding this! If I'm reading this correctly, I think the skip-parent comment is incorrect? Part I sec 2 says "The positions of the stars in the union of the flag and in the union jack shall be as indicated on the attachment to this order, which is hereby made a part of this order", and I think the attachment is the "Standard proportions" diagram at the top of page 3.
- deleted 4y ago
  [deleted]
amelius 4y ago
Since the star has 5 vertices, perhaps a pentagonal tiling looks better? https://en.wikipedia.org/wiki/Pentagonal_tiling https://en.wikipedia.org/wiki/Pentagonal_tiling
jamesrom 4y ago
I'd like to see more patterns than just different sized rows. What would a polygon packing algorithm produce? Say constrain all stars be equal size, but as large as possible.
- jbj 4y ago
  like this? https://en.m.wikipedia.org/wiki/Betsy_Ross_flag https://en.m.wikipedia.org/wiki/Betsy_Ross_flag
madcaptenor 4y ago
Glancing through the results, some only have really awkward arrangements, like 29 or 47. There was never officially a 47-star flag - the 47th and 48th states, New Mexico and Arizona, were admitted about a month apart, and the flag only updates on July 4. There were some 47-star flags made, though - mostly in New Mexico - and it looks like they mostly did 6-by-8 rectangle with one star missing and the corresponding row shifted. There was officially a 29-star flag for a year (between the admission of Iowa and Wisconsin), though. These rules suggest 10+9+10, which won't work in practice; some cursory Internet research suggests that some people used 8+7+6+8 and some people just did all sorts of weird things.

55 points by jbm 4y ago

> I limited the iterations to values of w between h and 5h (which still allows for really too oblong arrangements for higher values...) and listed only totals up to 200 stars, allowing for really aggressive Manifest Destiny scenarios and/or Balkanization within the current borders. Unfortunately if we tried to achieve senatorial parity by giving all states an equivalent population to Wyoming, ~664 states would be necessary. Fortunately the author gives recurrence relations, so even unlisted numbers of stars are, as per the title, arrangeable.

Mountain_Skies 4y ago
Plus the name of the country would need to be changed to the United Electoral Districts.

w-m 4y ago

Here's an advent of code puzzle for ya: build a page with four giant renders of the flag (q⃰, e⃰, p⃰ and r⃰), live updated by a slider that goes from 1 to 200. If there's multiple solutions for a certain pattern given a number of stars, choose the one that leaves the least amount of empty space around the stars. :)

Javantea_ 4y ago

This helps answer a serious argument I had on whether Puerto Rico and/or Washington D.C. should become states. Some people argued that the the flag could stay the same. I think the most clever answer would be to make a flag with a star randomly placed to annoy flag-obsessed nerds. More seriously, I think the reason that a 51st or 52nd state can't be added is that the urgency of the matter is lacking. Doing something about statehood would require it to be exceedingly popular and even then the odds are poor.

cratermoon 4y ago
> think the reason that a 51st or 52nd state can't be added is that the urgency of the matter is lacking. The reason for the resistance to statehood for Puerto Rico and D.C. is because they both lean heavily Democratic, and the prospect of 2 or 4 more Democratic Senators is unacceptable to the Republicans.
- friend_and_foe 4y ago
  I don't think that's the entirety of it. DC becoming a state is significantly more problematic than just the politics of it's residents, it's potentially unconstitutional. It makes more sense to cede the city outside the capitol to Maryland and Virginia and allow for representation that way (and what IMO should've been done instead of giving DC 3 electoral college votes via a constitutional amendment), and an amendment to make DC a state would require a lot of reorganizing, the clause providing for a 10 by 10 square mile federal district, the reasoning that the sovereignty of the united states can't be under jurisdiction of a state, it's just messy. Puerto Rico, I think the political balance between parties is largely the prohibiting factor, you're right. But there are other issues, they are not compliant on a lot of requirements for statehood as per US law (congress has the power to regulate this with any legislation), and it seems the status quo in Puerto Rico is exactly what the more powerful political and financial interests there want.
  - cratermoon 4y ago
    > they are not compliant on a lot of requirements for statehood as per US law (congress has the power to regulate this with any legislation) Hmm, I wonder how those laws got to be that way. It's a mystery.
    - friend_and_foe 4y ago
      Say what you mean. Puerto Rico has blatantly unconstitutional gun laws. It has a minimum wage under the federal minimum wage. The US congress requires all applicant territories for statehood have constitutions compliant with the US constitution (a problem for North Dakhota until 1997 funny enough), have laws requiring child support on the books and a whole host of other laws. Puerto Rico is compliant on some fronts and not on others.

friend_and_foe 4y ago

A lot of people don't know this, but there's actually no laws or rules about how you have to arrange stars on the flag, other than that they have to be white on a blue field. You can have a flag with one big star in the middle and 49 tiny stars around it, and it is valid as the US flag, you can have a mess of them, they can be upside down or sideways. I don't just mean the government can decide, I mean that you can make a flag like this and fly it and it is the US flag. Convention dictates though that all stars be of the same size, symbolism for the states all being equally co-sovereign over the union, and the arrangement revealed after a new state joins the union is usually what gets manufactured and becomes the not so official "official" flag.

chrisshroba 4y ago
I believe you, but do you have a source so I can read more?
- macintux 4y ago
  Not the OP, but this looks like the definitive resource. Still skimming it myself out of curiosity. https://www.govinfo.gov/content/pkg/USCODE-2011-title4/pdf/USCODE-2011-title4-chap1.pdf https://www.govinfo.gov/content/pkg/USCODE-2011-title4/pdf/U...
  - deleted 4y ago
    [deleted]
  - pinkmuffinere 4y ago
    Thanks for finding this! If I'm reading this correctly, I think the skip-parent comment is incorrect? Part I sec 2 says "The positions of the stars in the union of the flag and in the union jack shall be as indicated on the attachment to this order, which is hereby made a part of this order", and I think the attachment is the "Standard proportions" diagram at the top of page 3.
deleted 4y ago
[deleted]

amelius 4y ago

Since the star has 5 vertices, perhaps a pentagonal tiling looks better? https://en.wikipedia.org/wiki/Pentagonal_tiling https://en.wikipedia.org/wiki/Pentagonal_tiling

jamesrom 4y ago

I'd like to see more patterns than just different sized rows. What would a polygon packing algorithm produce? Say constrain all stars be equal size, but as large as possible.

jbj 4y ago
like this? https://en.m.wikipedia.org/wiki/Betsy_Ross_flag https://en.m.wikipedia.org/wiki/Betsy_Ross_flag

madcaptenor 4y ago

Glancing through the results, some only have really awkward arrangements, like 29 or 47. There was never officially a 47-star flag - the 47th and 48th states, New Mexico and Arizona, were admitted about a month apart, and the flag only updates on July 4. There were some 47-star flags made, though - mostly in New Mexico - and it looks like they mostly did 6-by-8 rectangle with one star missing and the corresponding row shifted. There was officially a 29-star flag for a year (between the admission of Iowa and Wisconsin), though. These rules suggest 10+9+10, which won't work in practice; some cursory Internet research suggests that some people used 8+7+6+8 and some people just did all sorts of weird things.