Math 305 – Dr. Bowen Brawner

Class Daily Averages(12/7/09)

Protractor

Choose 6 of the activities below.

Nets	W
Building polyhedra	W
Views 1	W
Views 2	W
Guess the view	W
Rotating views	W
Rotating houses	W
Building houses 1	W
Building houses 2	W
Build by night or day	W
Cube houses	W
Walls	W
Lathe	W
An impossible object	W
Volume of a box	NCTM
Isometric drawing	NCTM
3D TicTacToe	JaVaOnTheBrain

Numerical Prefixes

In this page, I discuss a curious set of unusual words: adjectives and nouns for numerical values or multiples. What do you call a group of eleven musicians? An athletic competition with six events? An event that recurs every twenty years? It can be very difficult to figure out what sort of prefix to use, and there are plenty of exceptions to the rules. Because many of these words aren’t found in dictionaries (particularly as the relevant numbers get larger), having some general principles can help. Thus, where other word lists of the Phrontistery are simply listed in “word: definition” form, this page will try to show you, in tabular format, how to construct your own terms from the basic principles, and to give you a better grasp of this tricky topic. Let’s begin!

In general, these words are made by combining a prefix derived from Latin or Greek number words and a suffix indicating the type or category of the thing being counted. If you know a lot of word etymologies, you can usually figure out whether a word takes a Latin or Greek numerical prefix if you can tell whether the suffix you want to use is Latin or Greek in origin. However, if you can’t work out the etymology, it’s probably best to just look at the lists below, which indicate which prefixes are used with which suffixes. Besides, there are exceptions to this general rule.

Latin prefixes (uni, bi, tri …) are normally used for the following categories.

mathematical bases “-al”
adjectives of relation “-nary”
groups of musicians “-tet”
words for multiples of something “-uple”
number of years between two events “-ennial”
number of sides of something “-lateral”
words for large numbers / exponents “-illion”
less common categories: number of leaflets or petals on a leaf or flower “-foliate”, chemical valencies “-valent”; division into parts “-partite” or “-fid”.

In this first table, I’ve listed the Latin words for 1 through 12 along with the appropriate prefix that is derived from it. For each of the above categories, check the appropriate column and find the word list. In cases where the word couldn’t be found in regular dictionaries, I’ve extrapolated from the other words and used appropriate prefixes and endings to construct the correct form. In such hypothetical cases, the word is marked with an asterisk and put it in italics.

TABLE 1: LATIN-PREFICED NUMERICAL WORDS

	Numeral	Prefix	Base	Relation	Music	Multiple	Yearly	Sides	Exponent
1	unus	uni	N/A	unary	(solo)	(single)	(annual)	unilateral	(million)
2	duo	bi/duo	binal	binary	duet	duple/double	biennial	bilateral	billion
3	tres, tria	tri	trial, tertial	trinary, ternary	trio	triple/treble	triennial	trilateral	trillion
4	quattuor	quadri/quart	quartal	quaternary	quartet	quadruple	quadriennial	quadrilateral	quadrillion
5	quinque	quinque/quint	quintal	quinary, quinquenary	quintet	quintuple	quinquennial	quinquelateral	quintillion
6	sex	sex(t), se	sextal	senary/sexenary	sextet	sextuple	sexennial	*sexilateral	sextillion
7	septem	sept	septimal	septenary	septet	septuple	septennial	septilateral	septillion
8	octo	oct	octal, octaval	octonary	octet	octuple	octennial	octilateral	octillion
9	novem	nonus/novem	nonal	nonary	nonet	nonuple, noncuple	novennial	*nonilateral	nonillion
10	decem	dec(a), de	decimal	denary	dectet	decuple	decennial	*decilateral	decillion
11	undecim	undec, unde	undecimal	undenary	*undectet	*undecuple	undecennial	*undecilateral	undecillion
12	duodecim	duodec, duode	duodecimal	duodenary	*duodectet	duodecuple	duodecennial	*duodecilateral	duodecillion

So far, so good. We can see that there are a few exceptions to the general rule, particularly for the numbers 1 and 2, and in some cases such as “quinary / quinquenary” where multiple forms exist. Since I’m not being hardline about “proper” forms, I’m including all the forms normally used, even when they don’t strictly follow the rules. Up to 12, the Latin prefixes hold up pretty well; most of the forms exist; only “sexilateral”, of all the hypotheticals, is less than nine. My theory is that it sounds too lewd to have been adopted as the term for something with six sides. Well enough, then. Let’s turn to the Greek prefixes (mono, di, tri …), which are used for the following categories:

number of sides of plane figures “-gon”
number of faces of solid figures “-hedron”
number of angles in a shape or line “-angle”
number of rulers in a government “-archy”
number of meters in a poetic verse”-meter”
number of objects in a group “-ad”
number of events in an athletic competition “-athlon”
less common categories: numbers of syllables in words “-syllabic”; sets of books or other works “-logy”; number of fingers “-dactylic”; number of languages spoken “-glot”; number of parts “-merous”; number of columns “-style”; amount of carbon in many chemical molecules “-ane”, “-ene”, “-yne”.

And now, Table 2 shows us the Greek numeral words and prefixes in conjunction with the appropriate suffixes for the above categories.

TABLE 2: GREEK-PREFIXED NUMERICAL WORDS

	Numeral	Prefix	Polygon	Polyhedron	Angle	Ruler	Meter	Group	Event
1	en	mono	N/A	N/A	N/A	monarch	N/A	monad	N/A
2	dyo/duo/di	di/dy	N/A	N/A	N/A	diarch, dyarch	dimeter	dyad	biathlon
3	treis, tria	tri	triangle	N/A	triangle	triarch	trimeter	triad	triathlon
4	tessera	tetra	tetragon	tetrahedron	quadrangle	tetrarch	tetrameter	tetrad	tetrathlon
5	pente	penta	pentagon	pentahedron	pentangle	pentarch	pentameter	pentad	pentathlon
6	hexa	hex	hexagon	hexahedron	hexangle	hexarch	hexameter	hexad	*hexathlon
7	hepta	hept	heptagon	heptahedron	heptangle	heptarch	heptameter	heptad	heptathlon
8	okto	oct	octagon	octohedron	octangle	octarch	octameter	octad	*octathlon
9	ennea	ennea	enneagon, nonagon	enneahedron	*enneangle	*ennearch	*enneameter	ennead	*enneathlon
10	deka	dec(a)	decagon	decahedron	decangle	decarch	decameter	decad(e)	decathlon
11	hendeka	hendec(a)	hendecagon, undecagon	hendecahedron	*hendecangle	hendecarch	*hendecameter	*hendecad	*hendecathlon
12	dodeka	dodec(a)	dodecagon	dodecahedron	*dodecangle	dodecarch	*dodecameter	dodecad(e)	*dodecathlon

The situation with the Greek terms is a little more complex than with the Latin, but not excessively so. Latin prefixes are used for some words for polygons, although the Greek prefix is to be preferred. “Biathlon” should, by all rights, be “diathlon”, “triangle” is used for a plane figure as well as angles (instead of ‘triagon’), and there are very few terms for 1 and 2. Of course, this is partly because there’s no such thing as a two-faced polyhedron, and not much point in describing a single athletic event as a “monathlon” …