### Friday, January 25, 2008

##
The Witch of Agnesi

What math teacher could resist a mystery titled

Well, the

If, say, we let

And why, you may ask, is this curve called the Witch of Agnesi? Well, therein lies the solution to the mystery.

Some students erroneously think that the name comes from the shape of the curve, which they somewhat dubiously imagine looks like a witch’s hat. Others think — and have thought over the centuries — that the curve is so-called because it was first discovered by Maria Agnesi, who was a witch.

Those people, at least, are half right, or maybe one-third right. The curve was actually discovered by Fermat, but it was published by the great Italian mathematician Maria Agnesi, who published it in 1748 in a book that MathWorld calls “the first surviving mathematical work written by a woman.” But the name of the curve — the key to solving the mystery — comes from a mistranslation, an event that warms the heart of anyone who has studied linguistics. Here we have slightly varying accounts. In the mystery novel, Spiller’s protagonist Bonnie Pinkwater (a math teacher, of course) explains the mistranslation to her precalculus class this way:

Unfortunately, however, Spiller himself may have gotten at least one of the words wrong. Then again, maybe not: as sources differ on the details (how appropriate that the devil is in the details in this case). The initial name for the curve is

Anyway, I seem to have gotten off the subject of reviewing the novel. You can see now why I just

Altogether a pleasant read, as they say — even though there isn’t nearly enough math in it.

P.S.: I suppose this seems to be yet another in my continuing series of reviews of novels that relate to high schools, but there’s an important difference between this one and the previous ones. In those earlier cases the school itself was a character in the novel, often in some sense the main character and usually an elite school. But Spiller’s novel is only incidentally school-related, and it’s clearly a very mixed-income and low-income public school, complete with students and teachers who live in trailer parks. Students are victims, and the protagonist is a teacher, and almost all of the characters are teachers, students, or parents — but it’s still not a book about a school, nor is it meant to be. Like most novels, it’s a book about people; the protagonist just happens to be a math teacher.

*The Witch of Agnesi.*Of course if you’re neither a math teacher nor a mathematician, you’re probably scratching your head right now, wondering, “*What is he talking about*?”Well, the

*Witch of Agnesi*is actually not the name of a witch, nor is Agnesi a town in Italy, as you might suppose. We need to digress for a moment to indulge in a brief math lesson, and then we can return to reviewing Robert Spiller’s mystery novel. Consider a curve that is described by the following equation:If, say, we let

*a =*2, its graph looks like this:And why, you may ask, is this curve called the Witch of Agnesi? Well, therein lies the solution to the mystery.

Some students erroneously think that the name comes from the shape of the curve, which they somewhat dubiously imagine looks like a witch’s hat. Others think — and have thought over the centuries — that the curve is so-called because it was first discovered by Maria Agnesi, who was a witch.

Those people, at least, are half right, or maybe one-third right. The curve was actually discovered by Fermat, but it was published by the great Italian mathematician Maria Agnesi, who published it in 1748 in a book that MathWorld calls “the first surviving mathematical work written by a woman.” But the name of the curve — the key to solving the mystery — comes from a mistranslation, an event that warms the heart of anyone who has studied linguistics. Here we have slightly varying accounts. In the mystery novel, Spiller’s protagonist Bonnie Pinkwater (a math teacher, of course) explains the mistranslation to her precalculus class this way:

“The famous French Mathematician [Passing over the discrepancy between Fermat (last name) and Maria (first name) — does that remind anyone of Obama and Hillary? — and the odd capitalization ofsic] Pierre de Fermat...had given the curve the Italian nameversiera,which simply means a curve that turns.... Maria used the same name...when she spoke of the curve in herAnalytic Institutions.She embellished and extended Fermat’s ideas, making large portions of the Mathematics her own.

“Now the scene shifts some fifty years hence. Maria Agnesi is dead. John Colson, a British Mathematician and linguist at Cambridge University, decides to translateAnalytic Institutionsinto English. He did an admirable job except for this one word.”

Nex toversierashe wroteaversieraand underlined the new word.... “He mistookversierafor this almost identical cousin...with disastrous results.... The wordaversierameans bride of the devil.”

*Mathematician*and*Mathematics,*we note how a single letter can make a big difference. But it’s still surprising that a linguist would miss an initial*a-*of all things. MacTutor provides the explanation: just remember to quote the noun along with its preceding definite article. It’s easy to mistake*la versiera*for*l’aversiera.*Unfortunately, however, Spiller himself may have gotten at least one of the words wrong. Then again, maybe not: as sources differ on the details (how appropriate that the devil is in the details in this case). The initial name for the curve is

*versiera*according to Spiller,*versiera*according to the reliable website MacTutor History of Mathematics, and*averisera*according to the equally reliable website MathWorld. Hmmm... And the erroneous reading by Colson was*aversiera*according to Spiller,*aversiera*according to MacTutor, and*avversiera*according to MathWorld. So maybe Spiller is right. This bears further research; stay tuned.Anyway, I seem to have gotten off the subject of reviewing the novel. You can see now why I just

*had*to check the book out of the library and read it. In general it’s a competent story that fits squarely into the traditional genre of the amateur private detective with a sidekick. As is traditional, there is a series of murders (or perhaps, being a math teacher, I should call it a*sequence*of murders; no summation is involved). As is traditional, there is effective use of red herrings. The plot is effective, even though it slows down in the middle of the book. The account of various Wiccan characters is sympathetic without being patronizing. There is a small amount of character development and suspense; one student, in particular, turns out not to be what he first seems to be — always a useful object lesson for teachers. The sidekick is altogether too much of a Sensitive New-Age Guy; I suppose he’s just as convincing as the nerdy science teacher in*Academy X,*but surely it’s not realistic to have a science teacher who’s a more sympathetic character than a math teacher. :-) The setting in eastern Colorado is convincing without being obtrusive. Finally, the ending is an effective surprise.Altogether a pleasant read, as they say — even though there isn’t nearly enough math in it.

P.S.: I suppose this seems to be yet another in my continuing series of reviews of novels that relate to high schools, but there’s an important difference between this one and the previous ones. In those earlier cases the school itself was a character in the novel, often in some sense the main character and usually an elite school. But Spiller’s novel is only incidentally school-related, and it’s clearly a very mixed-income and low-income public school, complete with students and teachers who live in trailer parks. Students are victims, and the protagonist is a teacher, and almost all of the characters are teachers, students, or parents — but it’s still not a book about a school, nor is it meant to be. Like most novels, it’s a book about people; the protagonist just happens to be a math teacher.

Labels: books, linguistics, math, teaching and learning

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