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Letters to Editors RE Tanton


Letters to the Editors/Author on
"A Dozen Questions about Pascal’s Triangle"

Letter #1

Dear Editors.

In "A Dozen Questions about Pascal's Triangle" (Math Horizons, November 2008, p. 5), James Tanton writes, "FACETIOUSLY is the only English word with each vowel (including y) appearing once and in order." With the recent economic downturn, perhaps abstemiously will return to common usage.

Deborah Gray
Concord Academy, Concord MA

Letter #2

Dear Dr. Tanton,

As usual, I enjoyed your dozenal article in the November Math Horizons. However, there are counterexamples to a couple of the claims in item #1 (Preliminaries). Besides FACETIOUSLY, the word ABSTEMIOUSLY also contains A, E, I, O, U, Y in order. I have also seen ARSENIOUSLY suggested, but it does not appear in my dictionaries, and turning ARSENIOUS into an adverb does seem somewhat forced. Of course, BOOKKEEPER and BOOKKEEPERS provide trivial counterexamples to the claim that BOOKKEEPING is the only English word with three sets of double letters. A nontrivial counterexample is SLEEPLESSNESS. The distinction of BOOKKEEPING and its cousins, as opposed to SLEEPLESSNESS, is that the sets of double letters are consecutive. I have even seen SUBBOOKKEEPER proposed as a word with four consecutive sets of double letters, but again, it is not in my dictionaries and seems a bit contrived. Once more, I enjoyed the article and look forward to the next in your dozenal series!

Leon Harkleroad

Response from the Author

A number of people have sent me e-mails and pointed out ABSTEMIOUSLY to me. There, apparently, is also a typo re the word BOOKKEEPING in that the adjective "consecutive" was missing. People have also pointed out that COMMITTEE has three sets of double letters.

It's nice to know that many people are reading the piece! (But I think I'll stick to mathematical claims in the future!)