# What comes after Quaternary?

Valorie asked me this question today, and I figured I'd toss it out to everyone who runs across this post.

She works in a 5/6 split class, and they're working on a unit on patterns and functions.  They're ordering the data into columns, each of which is derived from the information in the previous column.

The question is: What do they label the columns?

The first couple are obvious: Primary, and Secondary.

Third and fourth: Tertiary, Quaternary.

But what's the label for the fifth and subsequent columns?

AskOsford.com suggested that they use quinary (5), senary (6), septenary (7), octonary (8), nonary (9) and denary (10), using the latin roots.

But the teacher in the class remembers a different order and thinks that the next one (5) should be cinquainary (using the same root as the poetry form cinquains).

Valorie also pointed to  http://mathforum.com/dr.math/faq/faq.polygon.names.html for a 2-page history lesson. Coolest fact she found: the "gon" part of the word means "knee" and the "hedron" means "seats" so a polygon means "many knees" and polyhedra means "many seats".

So does anyone have any suggestions?

1. Anonymous says:

When we had a whole school photograph taken the teacher described it as a quinquennial event. I’d never heard the expression before, but it made sense straight away.

Looks like its a real word anyway

http://dictionary.reference.com/search?q=quinquennial

2. Anonymous says:

Personally I’d go with quinary etc. — it’s more likely to mean something to someone unfamiliar with the word (quintet is a common enough term). Cinquainary, nice though it may sound, would have meant nothing to me had it not had some sort of context, although I may have guessed at 50 or 500, as it looks vaguely like "cinquecento"…

3. Anonymous says:

About polygons, one of the standard screensavers installed with Ubuntu Linux shows all the 3D polygons in order with their proper names and vertices. I found it so fascinating that I just sat and watched it for a while.

As a child I used to play with Polydron

http://www.polydron.co.uk/cgi-bin/qsearch.cgi?itemcode=se&search=Polydron+Construction

sets, I only had the Equilateral triangles and squares, but found you could make some quite large solids using just those in repeating patterns.

4. Anonymous says:

How about 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ðŸ™‚

5. Anonymous says:

Latin was many, many moons ago. Lessee if I can remember:

primus, secundus, tertius, quartus, quintus, sextus, septimus, octavus, nonus, decimus.

So.. following the pattern I would have to guess: quintinary, sextiary, septimary, octavary, nonary, decimary.

6. Anonymous says:

cinquainary is how I have heard the 5th go as well, and is the one I’ve always used.

7. Anonymous says:

There is also an interesting etymological fact about the latin and greek words for five, quinque and pente: Latin que and greek te both mean "and", and latin quin and greek pen both come from the root of the word for "thumb". So, when you count to 5 in greek or latin, you actually say "one, two, three, four, and thumb."

8. Anonymous says:

This reminds me, it _really_ bugs me when people use "ternary" when they mean "trinary". "Ternary" is a synonym for "tertiary" (third in a sequence). "Trinary" means three-way (just as "binary" means two-way). So ?: is a trinary operator, not a ternary operator.

</pedantic-vent>

9. Anonymous says:

I would go with Pentiumnary, Pentiumtwonary, Celeronary, Octonary, and then Nunnery.

10. Anonymous says:

Bob, where does Itaniary fit in?

11. Anonymous says:

Itaniary sounds like ten, and I missed that one, so there you go *cheesy grin*

12. Anonymous says:

Mike, the OED and American Heritage dictionary both disagree with you. Ternary can be a synonym for /either/ trinary or tertiary, depending on context.

13. Anonymous says:

Pentium & friends comes from the Greek numbering prefixes, which are used in chemistry btw. Sorry, but deca is the prefix for 10 (quite similar to the Latin prefix for 10).

Does anybody know where ‘Itan’-comes from? Or did they just make up that part of the name…

14. Anonymous says:

Yes, Itan comes from the word "to tan". Fact is, them Itaniums get so hot that if you sit in front of one, you might get a tan. Therefore: I tan = Itan. ðŸ™‚ Totally made up, of course.

btw: I would go with quinary. Cinquinary sounds (and probably is) French. Since we use Latin base (or else it would have been troisary or something like that for the 3rd), mixing in French is odd…

15. Anonymous says:

Ugh! IMHO, if you have to use words like "quinary", you’re not approaching the problem mathematically. You shouldn’t be talking about the quinary column at all; you should (by the time you’ve got that far) be abstracting the problem to talk about the n’th column. So call them first-order, second-order, n’th-order.

It’s a bit like the programming rule that there are only three numbers: zero, one and infinity.

16. Anonymous says:

I’m glad they stopped at Pentium. I mean, would you really want a CPU called the Hexium or, even worse, Sexium? ðŸ˜‰

17. Anonymous says:

This has been fascinating. These guys are only 5th and 6th graders so the nth column is a bit beyond them. Some of the kids have no problem with variables and some have not yet developed to handle them. I can say ___ + 3 = 4 or ? + 3 = 4 and they are great but the minute I say x + 3 = 4, the language and math centers get horribly confused and they just drool ðŸ™‚

I think I’m glad that there isn’t a strong consistency. While the cinary sounds strange, I guess it’s the right one to use.

BTW, the kids got to choose to solve a pattern either in the the x^5 or x^9. Coolest thing? About a third of the kids chose to try the x^9 pattern.

18. Anonymous says:

Sorry, I saw the reference to a "5/6 split class", but I didn’t know what it meant (still not sure — ten/eleven years old?). I assumed that if you were using words like quaternary they’d be older, but of course long words like that are fun for kids of all ages ðŸ™‚

19. Anonymous says:

Following Oxford’s system though, I still can’t figure out what the 11th, 13th & so on systems would be called.

Does anybody know??

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