A new and improved version of my South America mnemonic and lesson and an easier puzzle.

This is my second published version of this mnemonic and puzzle. The mnemonic is essentially the same, but I tweaked it significantly. This article contains everything that was in the first article so there is no point in reading that one if you can read this one.

It’s a better, easier puzzle now.

When the order is used as puzzle to be explained, it is now an easier puzzle.

Here’s a puzzle: Why did I order these nations in this order and number them like this and why do I think that this numbered list is awesome? If you know the answer to the first version of this, the answer will be obvious. But you might try to figure out what exactly makes the new version so much better. My thoughts on that are below.

1. Colombia
2. Peru
3. Chile
4. Argentina
5. Brazil
6. Venezuela
7. Guyana
8. Suriname
9. French Guiana (I call it ‘France’)
10. Bolivia
11. Paraguay
12. Uruguay
13. Ecuador

Have a think and look at the map.

If you visit the website you can click on the map and see a very large high resolution version of the map.

Large detailed political map of South America with roads | Vidiani.com | Maps of all countries in…

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The list is intended to be used as mnemonic for the nations.
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More than one principle is involved.
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Memorizing the list helped me memorize not only the nations themselves but something else found in South America.

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On, close, in between,
On, close, very close.

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Cut by, missed by, flanked on both sides by, something.

Cut by, missed by, missed by a smidgen by, something.

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On, close, in between, (3, 3, 3)
On, close, very close. (2, 1, 1)

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The borders matter. The cities, roads, mountains, and so on do not.

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The names of the countries do not matter.

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The list also helped me memorize the lines of latitude and longitude, or as I call them, the parallels and meridians.
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Which countries share a border?
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Here’s the list divided into the subgroups that it is made of.

1. Colombia
2. Peru
3. Chile

4. Argentina
5. Brazil
6. Venezuela

7. Guyana
8. Suriname
9. French Guiana (I call it ‘France’)

10. Bolivia
11. Paraguay

12. Uruguay

13. Equador

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Which countries are bigger or smaller in area compared to their neighbors?
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Pay attention to the meridians (and some to the parallels) that are multiple of 15 degrees (these are the ones that are marked on the map), including the equator.
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Ignore islands, and pay attention to where the major meridians (and sometimes the parallels) just miss or cut nations.
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Ask youself which countries are cut by the 75th meridian west.
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Ask yourself which countries are just missed by a smidgen by the 75th meridian (west).
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Which countries lie between a pair of major parallels without getting hit by either of them?
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Which countries lie between the equator and the 15th parallel north?
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The answer (an awesome mnemonic IMHO):

The primary principle and the original inspiration for the mnemonic is the memorable relation of the major meridians and parallels (those that are multiples of 15 degrees and visible on the map provided) that cut South America to the borders of the first eleven countries in the list. Besides that, there is the way that the first nine countries in the list form an unbroken chain.

All the nations in South America that are cut by the 75th meridian:
1. Colombia
2. Peru
3. Chile

All the nations in South America that are just missed on the west by it:
4. Argentina
5. Brazil
6. Venezuela

All the nations in South America that are lying between the equator and the 15th parallel north that haven’t been mentioned yet:
7. Guyana
8. Suriname
9. France

All the nations that are cut by the 60th meridian that haven’t already been mentioned:
10. Bolivia
11. Paraguay

All the nations in South America that are just missed by the the 60th meridian and haven’t been mentioned yet:
12. Uruguay

All the nations in South America that are just missed on the east by the 75th meridian:
13. Ecuador

In short:

On, close, in between, (3, 3, 3)
On, close, very close. (2, 1, 1)

Since French Guiana (also known as Guyane) is an integral part of France, I will from now on refer to it simply as ‘France.’ This makes everything a lot easier to learn. I’m not saying it *should* be part of France, only that it *is* part of France at the moment. I discuss this a bit more, further down.

Other regularities in the list.

There is an imperfect but nevertheless memorable pattern in the magnitude of the area of the each nation in the list. That this could be used as part of the mnemonic was only noticed after the first version had been finished. It is purely fortuitous but still very useful.

a) The first nine form a chain. The biggest link is Brazil and is in the exact center, being #5. 6–9 are smaller and smaller while 4–1 are (with the sole exception of Chile, which is too small) also smaller and smaller. Thus the chain (except for the Chile problem) can be thought of as Brazil and it’s two tentacles. 1–6 and hence 1–3, and 4–6, have the property of ‘lacking a redundant link’, for want of a better term, meaning that Colombia cannot touch Chile, Peru cannot touch Argentina, Brazil cannot touch Chile, and Venezuela cannot touch Argentina. Put more concisely, Chile cannot touch Colombia or Brazil; Argentina cannot touch Peru or Venezuela. Furthermore, 1–6 is a ‘neatly folded’ chain, meaning 1 touches 6, 2 touches 5, and 3 touches 4 (of course). These two properties allow one to deduce a lot (all?) of the connectivity of the first six links of the chain and some adjacent countries. The remaining links 7–9 have a very simple topology that can easily be described and is naturally memorable.

b) Paraguay is smaller than Bolivia.

c) Uruguay is smaller than Paraguay.

d) Uruguay and Ecuador are the two loners. Each is bordered by the sea and two much larger nations. But Ecuador is cut by the equator, while Uruguay in cut by neither meridian nor parallel, though is close to (just missed by) the 60th meridian.

e) Peru is #2 while Uruguay is #12. So they both end in ‘2’ and they both contain at one end an ‘ooh’ sound that rhymes with ‘two’. They are also one place away from an end of the list. These odd facts may help with recalling that Peru and Uruguay have in common that they are both so closely missed by the equator and the 30th parallel respectively that at least one map shows them both as hit by those parallels.

Miscellaneous thoughts on the list and the map of South America.

This should probably be in an appendix because it seems to distract from the list, especially once Peru and Uruguay are digressed from. In my imagination, and maybe yours now, Peru is like a huge boot that points to a football. Note the ‘ooh’ sounds in ‘huge’, ‘boot’, and ‘football’. By the way, doesn’t it look like the football is getting kicked by an even bigger boot, Brazil? And the two boots seem to both tied together by their laces and draped the one locker room peg, don’t they. The peg might be Bolivia, one of the two countries to border both boots. Or are the boots hanging from Colombia, the other nation to border both boots. Colombia and Bolivia are #1 and #10. The difference between them is zero, ha ha. Their names are just a few letter changes away from each other. They are incredibly similar in size and shape. Colombia is named after Columbus and Bolivia is named after Bolivar. I wonder why I find this activity so compulsive? Let me know in the comments how interesting or otherwise these stream of consciousness thoughts are.

Why the second version is better than the first.

The order of the nations in the first version is which is not too bad except for the numbering:

1. Ecuador

2. Colombia
3. Peru
4. Chile

5. Argentina
6. Brazil
7. Venezuela

8. Guyana
9. Suriname
10. French Guiana

11. Bolivia
12. Paraguay

13. Uruguay

The problem with this is that the groups of three are numbered in such a way as to obscure the groups somewhat. Subtracting one from each number and putting Ecuador at the end, numbered 13 fixes this:

1. Colombia
2. Peru
3. Chile

4. Argentina
5. Brazil
6. Venezuela

7. Guyana
8. Suriname
9. French Guiana

10. Bolivia
11. Paraguay

12. Uruguay

13. Ecuador

Now the new 1 to 9 is much simpler and more regular in shape and therefore easier to visualize. Also, it can be thought of as a handwritten lower case ‘r’ or a handwritten lower case ‘v’, depending on whether you draw the line along the western tips of 4, 5, and 6, or through their middles or eastern tips.

There are some very small drawbacks to the renumbering:

a) We no longer starting with Ecuador, which spoils the pattern of starting to the west of the 75th meridian and moving progressively to the east. Now we start with the three nations *on* it, and Ecuador becomes a sort of leftover. But this doesn’t matter because Ecuador, being the only nation to the west of the meridian is in fact a natural loner, perhaps just as much as Uruguay is.

b) We can no longer say that the 45th parallel cuts only nations 4 and 5. Those two are now 3 and 4. That is a pity.

c) The nations cut by the Equator are 13, 1, and 5. That’s not as memorable as ‘1, 2 , 6’, but it’s not a big deal. O the other hand, the nations cut by the 30th parallel are 3, 4, and 5. That calls to mind the famous ‘3, 4, 5 triangle’ and is thus memorable. Also, 2, 10, and 5 lie on the 15th parallel which I find I can recall by thinking, ‘two goes into ten five times’.

Why is Ecuador not the ‘zeroth’ country in the list?

Some readers may wonder why I didn’t give ‘number zero’ to Equador. The reason is that I think it would be a controversial thing to do, and I am myself very much worried by what happens to the other numbers if zero is thought of as the first number. Is one then the second number? And is two the third number?

Having some but not all people using zero as the first number would cause widespread confusion, surely? ‘Day One’ would mean the second day to some, and the first to others. I once saw a book with a ‘Chapter 0’ in it. I can see that, arguably, zero should have been the first number all along, but I am not willing start using it that way for the reasons I already stated. I can see the temptation to squeeze in an extra item at the beginning of a list by calling it the ‘zeroth’ item, but it is not worth it, in my view. I would not do it, not even as a joke. I could be wrong, but until someone convinces me that I am, I will at least err on the side of caution.

And I just noticed that, now, 1 to 9, which is the analogue of 1 to 10 in the first version, is unlike the latter, symmetrical, with Brazil at the exact centre. If Ecuador were prepended to it, the symmettry would be spoiled.

Other stuff.

To fix in the student’s mind that Colombia is first in the list, how about merging ‘one’ and ‘Colombia’ thus: Onelombia, 1lombia, Colombione, or Colombi1? And likewise with all the rest, up to Thirteendor, 13dor, Ecthirteen, or Ec13? By referring to the nations by these names some of the time, the student will learn by osmosis the number of each nation, and nation of each number.

Additional coincidences in South America related to the 60th meridian.

This meridian as mentioned cuts Bolivia and Paraguay in a fairly remarkable way, seeming to stitch them together. It does the same thing but even more remarkably with Venezuela and Guyana just touching the eastern and western tips respectively. And see how after Bolivia and Paraguay it passes through Argentina, while after Venezuela and Guyana it passes in remarkably similar fashion through Brazil. These coincidences don’t get highlighted as much as they could have been in the mnemonic because it seemed to me more important to keep Venezuela, Guyana, Suriname, and France consecutive in the list. Bolivia and Paraguay are not of great interest to most people, because they have not heard of them, perhaps because those two nations are landlocked. I did consider having Bolivia follow Venezuela, but decided against it for the above reasons.

Not relevant to the mnemonic because it applies only to the mainland of South America, but it seems remarkable that the 60th meridian manages to hit exactly two islands of the Falkland Islands and exactly two islands of the South Shetland Islands. Not sure whether they are part of South America, anyway.

The 60th meridian cuts South America into two fairly equal areas. One could perhaps usefully refer to the areas to the east and west of the meridian as eastern South America and western South America or as areas east of the 60th meridian and west of the 60th meridian. The 60th meridian is roughly speaking where South America is longitude wise.

I just noticed another regularity. 4gentina, 5zil, and 6nezuela are all cut by the 60th meridian, though they are not the only ones to be so cut. They are each cut fairly near to (very near in the case of 6) its eastern tip. The 60th meridian cuts off about 10 percent of Brazil on the west, and about the same percentage of Bolivia but on the east.

It’s worth noting that 6nezuela, 7na, 8riname, and 9nch Guiana are, besides being north of the equator and south of the 15th parallel, entirely due east of each other. I mean every part of 7na, 8riname, and 9ch Guiana is due east of some part of 6nezuela, and every part of 8riname and 9ch Guiana is due east of some part of 7na, and every part of 9ch Guiana is due east of some part of 8riname. Note: I’ve ignored islands throughout and am not sure whether that makes a difference. And 6nezuela, 7na, 8riname, and 9ch Guiana are all likewise due east of Colombia, which cuts the equator.

60th meridian west

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en.wikipedia.org

What about the 45th meridian?

The 45th meridian is very roughly where the east coast of South America could be said to be. But the east coast is hard to pin down. I am mentioning the 45the meridian because it should be the opposite number of the 75th meridian. Also, it a very important meridian simply due to the fact that it is one eighth of the way around the earth from the prime meridian.

In South America, it cuts only Brazil, cutting off about a quarter of Brazil, which is about an eighth of South America, therefore. The point where it cuts the equator is fairly near the coast of Brazil. More interesting is the way it passes north to south neatly between Rio de Janeiro and Sao Paulo while the tropic of Capricorn passes west to east even more neatly between those two greatest economic powerhouses of Brazil. It’s as if the 45th meridian and the tropic of Capricorn form a pair of cross hairs on the area of greatest population and economic productivity in the country. ‘Rio de Janeiro has the second largest GDP of any city in Brazil, surpassed only by São Paulo.‘, says Wikipedia.

Also I see it hits Powell Island of the South Orkney Islands. Not sure whether they are part of South of America. Given that we saw that the 60th meridian hits exactly two of the Falkland Islands, and exactly two of the South Shetland Islands, it is really something that the 45th meridian hits Powell Island of the South Orkney Islands, because these islands are all of them small and few and far between.

45th meridian west

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en.wikipedia.org

“The doth root of yell.”

The word ‘doth’ is one I coined on the model of ‘eighth’, ‘nth’ and so on. It is pronounced ‘dot-th’ just as ‘eighth’ is pronounced ‘eight-th’.

To understand the following paragraph, it helps to know what the ‘nth root’ of something is.

Besides a handwritten three-stroke lowercase ‘r’ or ‘v’, a mathematical root sign sometimes has three strokes and is thus the shape, roughly, of the long chain of nations from Colombia to France. Hence, with Ecuador and Uruguay represented by a dot each, and Bolivia and Paraguay by a short line (i.e. a dash), the thirteen could be described as “The doth root of dash dot” or “The doth root of yell”. Bolivia, Paraguay, and Uruguay do make quite a good exclamation mark also known as a ‘yell mark’ or just as a ‘yell’.
In Morse code, dash dot stands for ’n’. So ‘The doth root of N’ could also be used as a name for the arrangement of the thirteen.

‘France’ is lot easier and is at least as good as ‘French Guiana/Guyane”.

“Guyana, Suriname, French Guiana” is very hard to learn. Since French Guiana is actually an integral part of France, we can instead commit to memory “Guyana, Suriname, France”. Much easier to say and spell. Much more interesting and therefore, memorable and thought provoking. This also gets rid of (postpones) the nagging question of whether to call it ‘Guyane’ or ‘French Guiana’. It’s really interesting that part of France is in South America. The European Space Agency launches its rockets into orbit from here because this part of France (and therefore of the EU) is so near the equator. This means that the ESA launches its rockets from France. It’s all the more interesting because so few people think about this, or even know it. Then ‘9. France’ could become ‘9nce’ or ‘9ce’ or ‘Ninence’ or ‘Ninece’ with all three rhyming with ‘pints’.

What to call the category that ‘9nce’ is an example of? ‘Numeronym’ is already taken, so we can’t use that. Is ‘diginym’ taken, I wonder?

‘7. Guyana, 8. Suriname, 9. France’ would then be ‘7na, 8riname, 9nce’ or ‘Sevenna, Eightriname, Ninence’, rhyming with ‘Ravenna’, ‘Vietnam’, and ‘pints’, respectively.

A hidden mnemonic and a separate additional mnemonic.

Just as a joke can be hidden, so can a mnemonic. It’s in effect a hidden meaning.

It might be fun or useful to teach someone the ordered set of thirteen countries without explaining the rhyme and reason of it. It could be learned by rote with or without any mention of the 3, 3, 3, 2, 1, 1 subgroups. In the latter case, it is harder for the student to notice the mnemonic coincidences. To make it harder still for the student to guess, one could have a completely separate different mnemonic.

If Argentina gave or sold about 600,000 square kilometers (a million would also do the trick) of land to Chile, the order by area of the first nine members of the list would be perfect. So this is really neat (except for Chile). I find it easy to recall a single exception to a rule. Let me know in the comments whether you also find it easy. This feature can be used as an explanation (strictly speaking bogus) for the order and/or be used a sort of mnemonic for it. It helps with recalling which countries share borders, and once you know that (except for Chile being about 600.000 square kilometers too small) the area gets bigger from 1 to 5, and then smaller from 6 to 9, and then with a dislocation, smaller from 10 to 12, you know a lot about the relative areas of the countries.

It’s then completely up to the teacher (or parent if it is used in homeschooling) when (if ever) to reveal to reveal the meridian and parallel based rationale behind the order, or indeed any of the regularities. It would be interesting to see how many students could learn the order without one of them noticing that it gives you knowledge of some of the parallels and meridians cutting South America.

Maybe students could be encouraged to think by asking them to look for patterns in my ordered list. In the process, the students would learn all about the map of South America.

A slogan or two to promote attention to parallels and meridians.

‘Make friends with meridians.’ ‘Pal up with parallels.’

How the South America mnemonic promotes numeracy.

Contemplating meridians and parallels is good for numeracy. So is merely using a numbered list. The groups of three are especially good for building numeracy. It isn’t immediately obvious how many numbers are in the range 4 to 6. Some will think it is two. It is good for numeracy to overlearn that 4 to 6 has three members, and likewise with the other subgroups. This will make students more numerate, and especially will make them better at avoiding the well-known ‘off-by-one error’. (‘OB1’, anyone?)

More stuff.

Suriname appears to be due north of Uruguay, with Uruguay due south of 7,8,9.

Peru is missed by the equator by 1' 48" says Wik/Geography of Peru/extreme points.

My favorite activity is learning new things.