Words No Longer Used

I’ve been listening to the audiobook of At Home by Bill Bryson, and there’s a segment where he talks about words previously used to refer to the bathroom. My favorite is

necessarium

with its Latin meaning of “necessity,” implying that a room dedicated to urinating and defecating may not be something we really want in our house but very much need.

This made me wonder about mathematical words that are no longer in use. Many have gone the way of necessarium, but I think they deserve consideration for reintroduction. Well, maybe not all of them. Let’s have a look…

octothorpe, n. : another name for the pound sign (#); the hashtag. Wouldn’t it be great if #worldoctopusday were read as “octothorpe world octopus day”?

surd, n. : a square root that cannot be reduced further. This word comes from its meaning in phonetics of “mute” or “voiceless” for an unvoiced consonant; in math, it refers to an expression that cannot be expressed (spoken) as a rational number. The following radical would be ab‑surd:

vinculum, n. : a horizontal line drawn over a group of terms in a mathematical expression that serve as a grouping, such as the line on top of a radical that indicates the number for which the root is to be taken, or the fraction bar, which appears over the entire denominator. Still used occasionally, but rarely.

Logo of Vinculum, a global software company.

solidus, n. : the diagonal slash “/” used as the bar between numerator and denominator of an in-line fraction. Also, a famous Roman bodybuilder.
synonym diagonal

virgule, n. : a diagonal slash resembling the solidus, but with slightly less slant, used to denote division for in-line equations. This is also the name for the line used to indicate a choice between two terms in writing, e.g., and/or or pass/fail.

lattermath, n. : aftermath. Okay, not really a math term, but on the list since it contains “math.”

porism, n. : an archaic type of mathematical proposition whose historical purpose is not entirely known. It is used instead of “theorem” by some authors for a small number of results for historical reasons.

Jacob’s staff, n. : a mathematical instrument used for measuring heights and distances; typically, a pole with length markings on it.

anthyphairetic ratio, n. : a continued fraction, such as

.

Same number of syllables as parallelogram and inequality, but cooler than either of those. If you looked at anthyphairetic and thought, “that’s Greek to me,” you’d be entirely correct.

XII Puzzle

Yesterday, my wife and I celebrated our 12th anniversary. We celebrated at home, with the boys and a home-cooked meal. I created the following puzzle to fill the time between dinner and dessert.

Each of the 12 answers in this puzzle is a 12-letter word that contains the letters X, I, and I, a reference to the Roman numeral XII. Those three letters appear in the proper order, though they may be separated by other letters.

For example, if you were given the clue, “Of or relating to the study of flags,” you would say, “VEXILLOLOGIC,” which consists of 12 letters and has X, I, and I as the third, fourth, and eleventh letters, respectively.

Below are the clues, each presented in two parts. The first part is the real clue, and the second part in italics is a fun addendum specifically for our anniversary.

Enjoy, and good luck!

1. Device for putting out a fire, like the one I needed when mommy set my heart ablaze.
2. Feeling of excitement or elation, like the feeling I had when mommy said, “I do!” (possibly arising from the trepidation that she might not).
3. Insufficient oxygen due to abnormal breathing, which I experience regularly when mommy kisses me.
4. Lowest part of the sternum, which holds in the abdominal diaphragm and prevents me from experiencing asphyxia when mommy is nearby.
5. Someone who takes money or other things through force or threats, which you might call mommy for stealing my heart.
6. State of being so happy (or drunk) as to lose control of your faculties or behavior, which is the state I’ve been in since I fell in love with mommy.
7. Someone who loves and studies words, like mommy and daddy.
8. Serving as an example, like how I serve as a warning to women about why they shouldn’t get married.
9. Someone who studies the adverse effects of chemicals on humans, like the scientist who told me that mommy’s love is as addictive as Vicodin.
10. Torturous, intensely painful, or mentally agonizing, which are three ways that mommy has occasionally described living with me.
11. To increase as much as possible, or the process of trying to find the best option, like the one I used to find the best wife in the world.
12. In the US, a 1 followed by 51 zeroes; in the UK, a 1 followed by 96 zeroes, or how much I love mommy on a scale of 1 to 10.

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Having trouble figuring out the answers? Well, I won’t give them to you, but if you search *x*i*i* at www.morewords.com, it’ll return all 666 words that contain X, I, and I in the proper order. That should significantly limit your search. You’ll then need to do a little work to figure out which 12-letter words fit the clues above.

Math and Prolific Writers in the 21st Century

The FAQ at the Folger Shakespeare Library, referencing Martin Spevack, claims that Shakespeare’s complete works consist of 884,647 words. Open Source Shakespeare claims that his complete works consist of 884,421 words. Whatever. I’m not going to split hairs over one-twentieth of a percent.

What do you get if you add 1 rabbit + ½ rabbit + ¼ rabbit + … ?
Two rabbits, but that’s just splitting hares.

Those numbers got me thinking. Shakespeare — or whichever “secret author(s)” actually wrote all that stuff — is often considered to be one of the most prolific authors of all time.

Yet here’s my typical annual output over the last 5 years.

Category	Number	Approximate Word Length
Email – Short	500	10
Email – Medium	1,500	100
Email – Long	50	1,000
Facebook Post	50	50
Blog Post	70	600
Journal Article	1	2,000
Math Joke Book	1/5	12,000

That translates to over 250,000 words a year, which means that I write the equivalent of Shakespeare’s 37 plays and 154 sonnets in about 42 months.

I mean, sure, Shakespeare’s typical lines are something like

For as the sun is daily new and old,
So is my love still telling what is told

whereas a line from my typical email is more like

I’d like to see the storyboard for the Featherless Birds interactive by the end of the week

but I’m not talking about quality here. I’m only referring to quantity.

And in that regard, Will, you got nothing.

Of course, he does deserve props for his occasional reference to math:

There is divinity in odd numbers, either in nativity, chance or death.
— The Merry Wives of Windsor, Act V, Scene 1

And whether deliberate or not, he had a penchant for 2 × 7:

So, sure, maybe William Shakespeare was not as prolific as I am. Or, for that matter, as prolific as most 21st century office workers who sit in a cubicle, stare at a screen, and bang on a keyboard all day. But he was pretty cool.

Better three hours too soon than a minute too late.

Math Hinky-Pinkies

A hinky-pinky is a phrase consisting of two rhyming words, such as fun run or tragic magic.

My sons recently brought home an activity sheet from school titled Stinky Pinky. It asked them to identify a hinky-pinky corresponding to a brief definition. Some examples from this sheet:

Cart for a Large Creature:
Dragon Wagon

The Robber in Charge:
Chief Thief

Odd Whiskers:
Weird Beard

The one that neither they nor I could figure out:

Dinner Party for Wild Animals

Any thoughts?

Completing this activity with them, I decided to create some math hinky-pinkies, where one of the words in each pair is a common math term. Here ya go, and good luck!

1. Low-Ranking Half of an Ordered Pair
2. Avoidance of Math Sentences
3. Calcium Carbonate Lecture
4. Decrease in Binary Operations
5. Dirty Three-Dimensional Object
6. Fat-Free Average
7. Internal Dissension Among Rational Numbers
8. Lust for Minuends and Subtrahends
9. Naked Quadrilateral
10. Odd Set of y-Values
11. Reddish-Brown Digit
12. Sudden and Extreme Second-Degree Polynomial
13. Slander Against an Iterative Process
14. Mentally Healthy Two-Dimensional Grid
15. Ice Cream Holder, All By Itself
16. Old and Tilted Item

For more fun with hinky-pinkies, check out this easy hink pink quiz.

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Spoiler… answers below.

1. Subordinate Coordinate
2. Equation Evasion
3. Chalk Talk
4. Addition Attrition
5. Squalid Solid
6. Lean Mean
7. Fraction Faction
8. Subtraction Attraction
9. Bare Square
10. Strange Range
11. Umber Number
12. Dramatic Quadratic
13. Recursion Aspersion
14. Sane Plane
15. Lone Cone
16. Oblique Antique

Square Deal

Recently, my twin sons Alex and Eli have taken a shine to crossword puzzles. They’re only 3½, but they love letters and words, so I started making up crosswords for them using a free online crossword puzzle maker. I construct clues based on things they know — for instance, REMY is the answer to the clue OUR DOG, and IDAHO is the answer to the clue STATE NAME WE CAN SPELL WITH OUR BATH TUB LETTERS. (They have a set of foam alphabet letters, but each letter A‑Z occurs only once, so it’s not possible to spell any words with repeated letters.) They don’t quite have the motor skills to write the letters, so they read the clues and spell the answers aloud as I fill in the grid.

Tonight, I asked if they’d like to help me make a crossword puzzle. I drew a 3 × 3 grid, and I asked, “To make a crossword puzzle, you have to fill in words both down and across. Can you give me a word with three letters?” Eli suggested TOW, which I used in the first row of the grid:

T	O	W

 

Then I asked, “Okay, so the word in the first column starts with a T. Can you think of a three‑letter word that starts with a T?” Never one to overlook the obvious, Eli suggested TOW again. I filled it in, and we moved to the middle column. “Can you think of a three‑letter word that starts with an O?” Alex suggested ONE. Eli immediately realized that we could now add an E at the end of the middle row to make ONE. At that point, eight of the nine squares were filled. I pointed to the third column. “Can you think of a three-letter word that starts with a W and an E?” Eli shouted WET, and the grid was complete:

T	O	W
O	N	E
W	E	T

 

Eli then pointed out that ELI contains three letters. “Let’s make another one!” he said. So we did:

W	E	T
E	L	I
T	I	E

 

Alex then requested that we make a 4 × 4 grid that included his name, and I was very impressed with the grid that they concocted:

I	O	W	A
O	V	A	L
W	A	V	E
A	L	E	X

 

I told you that story mainly because I like talking about my sons, but also because it leads me to a cool puzzle that I think you’ll enjoy.

Use the point values for each letter as in the word game SCRABBLE:

• 1 point: A, E, I, O, L, N, R, S, T, U
• 2 points: D, G
• 3 points: B, C, M, P
• 4 points: F, H, V, W, Y
• 5 points: K
• 8 points: J, X
• 10 points: Q, Z

Create a 4 × 4 grid composed of common English words (you can use the list of official Scrabble four‑letter words** as a reference) such that the sum of the point values of the 16 letters is as high as possible.

The 4 × 4 grid that my sons created would be disqualified, because IOWA and ALEX are proper nouns. That aside, it contains four A’s; two O’s, W’s, V’s, L’s and E’s; one I; and, one X. If it were acceptable, it would be worth 35 points.

I was able to create a grid with a sum of 62 points. I’m sure that better grids are possible. What’s the best that you can do?

** Special thanks to Veky Edgar, who pointed out that the list of four-letter words appearing on my web site was incorrect. The list has been updated, and I’ve stolen it from a more credible source this time, so I believe it is now correct.

5 New (Mathy) Words from the OED

The OED is the Oxford English Dictionary, the world’s largest dictionary of the English language (though not, however, the world’s largest dictionary — that distinction belongs to the Dutch dictionary Woordenboek der Nederlandsche Taal.) The OED attempts to “present in alphabetical series the words that have formed the English vocabulary from the time of the earliest records down to the present day.”

Forgive me if you already knew that. I just never assume that mathy folks know (or care) about the OED, just as I don’t assume that literary people are familiar with the Fundamental Theorem of Algebra.

The OED is revised four times a year. Over 2,400 entries were added during the most recent revision (December 1), and the following are new words that entered the dictionary during the past year:

• coordinate geometry – system in which points, lines, shapes, and surfaces are represented by algebraic expressions. This term was added as a “subordinate entry,” meaning that it appears under the main entry “coordinate.” Still, it’s surprising that it took four millennia to get the word into the OED (Descartes introduced the coordinate plane in Discourse on the Method of Reasoning Well and Seeking Truth in the Sciences in 1637).
• cyberslacking – using internet access at work for personal reasons while maintaining the appearance of working. For example, updating a math joke blog instead of revising the budget per your director’s request.
• ego-surfing – searching the web for instances of your own name. Or checking Amazon daily to determine the sales ranking of your book.
• Richard Snary – as Dick is a shortened form of Richard, this is a pun for “dictionary.” (Go ahead, say, “Dick Snary” out loud and listen to what it sounds like.) This is a 17th‑century slang term that has somehow hung around for several hundred years, not unlike the math pun, “Pie aren’t square, pie are round!”
• Rolle’s theorem – a theorem which says that a differentiable function with equal values at two points must have a point somewhere in between where the first derivative is zero. It’s good to see that calculus is getting some props.
• rope’s length – in knot theory, the minimal length of an ideally flexible rope needed to tie a given knot. What’s unclear is whether this is the intention for the entry in the OED. Knot theorists use ropelength, not rope’s length, to describe this concept, but a Google search fails to reveal any common use of “rope’s length.”
• techy – an informal way of designating technological sophistication. This is heartening — with techy now officially recognized, “mathy” can’t be far behind.

The following are entries that should be added but probably never will be:

• decagon – what a croupier says after being fired.
• dilemma – a lemma with two results.
• paradox – two wharves.
• protractor – in favor of farm machinery.
• tangent – a sun-burned gentleman.
• Calvin Culus, Albert Jabra, and Paulina Hedron – hey, if Richard Snary gets in for “dictionary,” then it’s only reasonable that we math folks get some stupid puns, too.

What’s in a Name?

The product value of a word can be calculated as follows:

Assign each letter of the alphabet a value as follows: A = 1, B = 2, C = 3, and so on. The product value of a word is the product of its letters. For instance, the word CAT has a product value of 60 because C = 3, A = 1, T = 20, and 3 × 1 × 20 = 60.

During a recent webinar, I introduced participants to my collection of Product Value Puzzles. The following product value puzzle is credited to John Horton Conway:

Find an English word with a product value of 3,000,000.

Finding the solution is up to you. But I will give you some good news — there’s not a unique answer. In fact, there are two English words that satisfy the conditions of the problem.

What most folks found interesting, though, are the Product Value Calculators on my web site. With these two tools, you can:

1. Enter an integer value, and the first calculator will return all words in the English language whose product value equals the number you enter.
2. Enter a word, and the second calculator will return the product value.

One of the participants during the webinar said that her middle school students, when confronted with any type of math puzzle involving words, will first apply the rules of the puzzle to their name. Apparently, I’m not much different from a middle school kid, because that’s what I did, too. Turns out, my name has a product value of 1,710,720:

Patrick = 16 × 1 × 20 × 18 × 9 × 3 × 11 = 1,710,720

So, then I wondered, “Are there any other words that have a product value of 1,710,720?” Of course, I could have used the Product Value Calculators to find the answer, but that would have been unsatisfying. With a little trial-and-error, I found that blackboard also has a product value of 1,710,720:

blackboard = 2 × 12 × 1 × 3 × 11 × 2 × 15 × 1 × 18 × 4 = 1,710,720

There were three things about solving this problem that I really enjoyed:

1. My strategy involved substitutions: I replaced a letter or a pairs of letters by other pairs of letters that have the same product value. For instance, the t and c in Patrick could be replaced by o and d, because both pairs have a product value of 60.
2. Calculating the product values for Patrick and blackboard reveal two distinct factorizations for 1,710,720.
3. How cool is it that I’m a mathy folk, and my name and blackboard have the same product value?

(Incidentally, my boss David found that his name and the word chalk have the same product value. Some would argue that its numerological destiny that we work together and are friends.)

So now I’ll offer  the challenge to you. Can you find a word that has the same product value as your name? Good luck!

Of course, if that’s more thinking than you care to do right now, you could just access the product value calculator. But what fun would that be?