# Mathematical Model Shows What Future Flags Would Look Like as U.S. Grows

Old Glory 51 bright stars and 13 broad stripes. Slate Magazine and an Emory University math professor have figured out how to preserve Old Glory's symmetry in case a new state is ever admitted to the Union. Slate

If Puerto Rico becomes a state, we'd have to add a 51st star to the flag. An Emory University mathematician has come up with a method to do it without disrupting Old Glory's symmetry.

The Puerto Rico Democracy Act of 2010, currently making its way through Congress, could make it it a necessity. The bill would grant the territory's residents a vote on their status, and options include statehood or independence.

Mathematician Skip Garibaldi analyzed the country's past flags to figure out the most common flag patterns, and worked out which patterns would work best for varying numbers of stars.

This interactive flag calculator allows you to come up with flag designs for states up to 100, with a couple exceptions.

You can also subtract states, which might come in handy if certain Texas politicians ever get their way.

As Slate's Chris Wilson explains, most flag designs arrange the star-spangle in ways that are vertically symmetrical, horizontally symmetrical, or both. This means the left half of the blue star field matches the right, or the bottom half matches the top. The current flag has both forms of symmetry.

Symmetry breaks in a 51-star flag, but the pattern would still look similar to our current design in that it's made of alternating rows. Most star configurations align each row of stars with gaps in the row above, making the stars less cramped, as Wilson explains.

Following those guidelines, there are six flag templates that can theoretically fit any number of states up to 100 -- except 29, 69 and 87. The "long" template involves alternating rows of even and odd numbers of stars, starting with the longer row. The "short" template is similar, but starts with the shorter row. In the "Wyoming" template, used after the 44th state was admitted to the Union, the first and last rows have more stars than the interior rows. Conveniently, this configuration also resembles the Equality State.

Using those templates, there are plenty of ways to make your own gallantly streaming star-spangled banners. And it's just in time for Flag Day on Monday.

[Slate]

LOL, the one for 69 stars looks pretty interesting.

LOL, the one for 69 stars looks pretty interesting.

regardless of how extremely liberal or conservative people may be, i think the idea of changing the VERY nice and even number of 50 states would not sit well with most.

Adding a state would require breaking up an existing one. I dont think many states would like that idea. Adding another one would seem to require some act of imperialism (except for PR i guess). lets face it, the US is big enough as it is and at least China is headed in the right direction with their 1-child policy. even though they have the largest pop. more countries should also adopt a similar policy....like India.

I think we stopped at 50, an island, for a reason. I think we're past adding/removing states.

51 is perfectly logical as Puerto Rico is in the same position as most past states. They are a US territory. same as Hawaii and Alaska once was. 51 or 50...whats the big deal? unless you have some sort of OCD with even numbers i don't see the problem. though it is true beyond 51 it would require some sort of imperialism to return, or some kind of peaceful civil war between states over some sort of policy...immigration or taxes of some sort.

Your views on big enough couldn't be more misguided. The US is no where near population saturation. with only just over 300million and yet one of the largest countries, land isn't a problem, nor is food.

we only stopped at 50 because we ran out of reasonable territories to make states, and with the option of populations in territories having the option to choose independence, some chose that route.

It will be interesting to see puerto Rico's choice. especially if the option to remain a territory is not reinserted into their list of options. I believe the ballot is still scheduled to have only independence or statehood as an option, much to the disappointment of the puerto Rican people.

How can you possibly say 300 million isn't too many? Just cause 1 Billion people could eek out a living in the US doesn't mean they should. There is a difference also between just feeding yourself and having a life. The ecosystems in the US are under enough strain as it is. Both coasts are paved already, whats the rush to pave the rest?

You must live in a city because maybe you think your environmental impact is limited to the 500 sq ft of your filing cabinet...I mean "condo".

The only reason food is not a problem is because you can import it from countries who have excess, that is fine as long as you have money but the US is losing ground on all fronts and this lifestyle change will be a hard pill to swallow for even the 300 million let alone 1 billion. Don't forget the US population lives on resources that come from all over the world, not just what is contained within its borders.

Considering the US produces enough food that it has to burn and dump portions of it each year, i don't think food is anything to worry about. And that is definitely something that you would assume i live in a city? I live in the suburbs, surrounded by corn and soybean fields. The only major import for America is materials- oil, minerals, etc, not food(excluding exotic foods and some seafood).

And adding states has nothing to do with population problems, maybe you need to reevaluate your definition big enough. Are you talking population or size? As you add states, you increase your land, so new population has no realistic effect.

Have you ever traveled the country? not the major cities, but the rest of the country, the other 95%. I'm not sure where your getting your facts from? I don't know where you find these ecosystems that are so strained by our over-population? (and the gulf doesn't count, because that's not population problems.)

Just so we are on the same page, you consider losing your life style of eating half a banana and tossing the other half more important than the lifestyle of having the freedom, the right, to have more than 1 child.

Your right the US does import oil which is the most important thing to remember, all other resources depend on it. When the cost of oil inevitably goes up you will find that your perceived excess is due only to cheap transport of shortage goods. Tough to get your fruits and vegetables in Chicago in January. If you want to eat corn all the time then your fine, why do you think people starve in China? Not enough rice?

Value added industry and manufacturing has been sold to China, pretty soon they will dictate terms and your corn farmers will sell to the highest bidders, those overseas with the cash. You wont starve but suddenly competing with millions of others for low paying service jobs isn't going to seem so cool anymore. Don't underestimate how much is imported from Canada, Hydroelectricity for the Eastern seaboard, Oil from Alberta, all sorts of minerals, seafood (especially now after the Gulf spill). Softwood lumber, which has to be tariffed so the American producers can stay competitive. Electronics from Japan and China, not to mention almost everything in your suburban home.

America is an amazing country but it's strength has always come from abundant resources, strong industry and a free entrepreneurial spirit. The industry has been sold off. The entrepreneurial spirit has been dulled by years of sloth and overindulgence and the resources always seem abundant until it's too late. Don't worry yet though, there's still the arctic oil in Alaska, just watch those pesky blowouts.

Ha ha, look at liming who posted above me, he has excellent grammar, I would imagine he graduated from Harvard (Beijing Campus). Get used to it.

Having more than one child is your right absolutely but the Earth reserves its right to cull your fertility drug induced progeny at any time due to war, famine, pestilence or insert your wrath of god here.

P.S. sorry for sidetracking this comment board with my lunacy.

An excellent tool for the truest adherents of Manifest Destiny out there. And by the way, dibs on "Manifest Destiny" as a band name.

most of what you just brought up is totally off topic, but i would just like to say the excess isnt due to price of cheap transport. its from economic floors and ceilings imposed on the farming industry. exports arent freely allowed either. So no worries about china jumping the gun on the us citizens on our corn.

Why can't Popular Science get rid of spammers like "liming" above?

Point: Nizeke.

USA - 5% of the world's population, 35% of the world's food production.

This is why when the US says it is going to put corn in her cars, there are food riots in the third world (countries that recieve millions in foriegn aid from the US every year - most of that foriegn aid in the form of free food).

This is why when there is a global tragedy, the US president can stand right up and pledge millions in aid - knowing that most of that aid will be food, which costs the country nothing to give, using European gifts to fund the transport.

This is why the US does not have to fear the global markets (China, India, etc). As those countries mature, their populations growth will level, but their food consumption will not (due to economic development leading to an increased intake of farmed meat - which requires much more "food quality" per pound of production).

True, right now the government still subsidizes farmers (grows crops to burn, dump, or give away). This keeps farmers farming. Otherwise, food prices would plumet - and this would only be a good thing for a short time, as farmers would quit, taking away the overproduction that is our countries economic foundation.

As for the flag, I'm wondering why they stopped at 100.

There are 31 potential states to the south who seem anxious to become American to quickly to wait. There are 7 other soveriegn states south of there that would also take a step up in becomeing less soveriegn states of the US.

There are 5 other good candidates in the carribian.

Then, of course, are the 13 states to the north as well.

That's 56 potential future states, not including PR. With the exception of the 13 Canadian states (provences and territories), it would be in the interest of the people to join (economically and politically). Also, opening up the states solves many signifigant US issues -

1) Jobs lost to NAFTA - back in the fold.
2) Illegal immigrants - legal now, and they don't have to move.
3) Drugs - US law enforcement in the southern states and a border to guard against Columbia that you can walk across in a day.
4) Energy independence - we buy most of our oil from Canada anyways, this just makes the tax issues easier.

Voluntary Empiricism is the Empiricism of the future!

(The reason the EU has had difficulties is because of individual soveriegnty dragging the strong nations down with the weak and credit-foolish, if the EU had instead become the national state of Franch or the national state of Germany - it would have worked much better - (as it did the last four times one of those countries controlled most of Europe)).

Like I said, enjoy eating corn.

Reasons PR should be a state by now!

- You can jump on a domestic flight to PR anytime and without a passport. You just need a valid drivers license or ID.

- PR(and it's surrounding islands) has the most beautiful beaches in the world

- PRicans are some of the most beautiful people in the world (especially the women)

- We already share our cultures, music, dance and languages

- They get to vote in primaries but not presidential elections. What's up with that?

- They are a viable economy. They will only grow our overall economy.

- The US will continue to grown and expand. There will definitely be more stars added to that flag, so let's get over it already. It is a good thing!!! The European Union does it everyday (adds stars to their flag).

- We either make them a state, or get the hell out of there and leave them alone. No in between. That's why they're so fed up.

IMHO

you should know in the past when this gets brought up, PR votes to remain a territory. its only a bigger issue now, because the current ballot wouldnt give them that choice, just state or free.

Colonialism isn't Equality! Maybe it's just a few steps above SLAVERY!!!...

I demand my right to VOTE and my Congress representation...

signed,
Second class American Citizen from Puerto Rico

As a Puertorrican my only comment is: where do I sign so PR becomes the 51st state?

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