### The Witch of Agnesi

June 22, 2010 The science fiction author and biochemist, Isaac Asimov had a simple test of whether a person was a scientist or a non-scientist. He would ask them to pronounce the word, "unionized." If they pronounced it with an initial*you*sound, as the word for a worker's collective organization, they were non-scientists. If they pronounced it with an initial

*un*sound, as un-ion-ized, then they were scientists. I have a similar test for mathematicians, and this test is made all the easier by the Harry Potter books. If a person thinks the "Witch of Agnesi" is a character from that sort of book, then he's not a mathematician. Mathematicians know that the Witch of Agnesi is a mathematical function. The Witch of Agnesi is a mathematical function first studied by Pierre de Fermat in 1630. It was popularized in 1748 by Maria Agnesi, the daughter of an wealthy Italian silk merchant. Agnesi published it in her two-volume treatise on mathematics, "Instituzioni analitiche," that contained more than a thousand pages. [1] The first volume concerned arithmetic, geometry, trigonometry, analytical geometry and calculus, while the second volume contained infinite series and differential equations. [1] The function is interesting because it can be constructed geometrically [2]. It is written, as follows: y = 8a

^{3}/(4a

^{2}+ x

^{2}) where a is a constant. For a = 1/2, this becomes y = 1/(1 + x

^{2}) The figure below illustrates the form of the curve.

*The Witch of Agnesi with parameter a=8, normalized to peak at y=1.*

How did this function get its name? Agnesi called it

*la versiera*. This is a nautical term for a rope that turns a sail [1], an allusion to the curve's geometrical construction. When her book was translated into English by John Colson, a Cambridge professor, he apparently misread the word; or his knowledge of Italian did not include such an obscure nautical term. He read it as

*l'avversiera*, meaning "witch." The Witch of Agnesia is a useful function, since it can replace the Normal Distribution in some mathematical models, and it can be easily integrated. As can be inferred from its simplicity, it can describe a number of physical systems, such as a driven oscillator near resonance. [1] Agnesi was the first woman appointed as a mathematics professor at a university; in that case, the University of Bologna, but it doesn't appear that she ever taught there. She left mathematics upon the death of her father and became a nun, founding homes for the poor, ill and elderly. [1] Isaac Asimov's book are cataloged in nine of the ten major categories of the Dewey Decimal Classification. He never wrote a book in the "Philosophy and Psychology" category. I would think, for a scientist, that would be the easiest category in which to publish. [3]

### References:

- This Month in Physics History: Circa June 1748: Publication of Analytical Institutions, American Physical Society Newsletter, Series II, vol. 19, no. 6 (June, 2010), p. 2.
- Witch of Agnesi on Wikipedia.
- Edward Seiler, Isaac Asimov Home Page, asimovonline.com.

*Permanent Link to this article*

RSS Feed

### Google Search

Latest Books by Dev Gualtieri

Thanks to Cory Doctorow of BoingBoing for his favorable review of Secret Codes!

Other Books

- Paving Materials - July 13, 2020

- 400 Years of the Novum Organum - July 6, 2020

- Isotropy of the Universe - June 29, 2020

- Bruce Baker and Minspeak - June 22, 2020

- Bottle Flow - June 15, 2020

- The Fine Structure Constant - June 8, 2020

- A Special Triangle Pair - June 1, 2020

- Philip W. Anderson (1923-2020) - May 25, 2020

- Worker Ants of Science - May 18, 2020

- Strength of Materials - May 11, 2020

- Spread Spectrum Communications - May 4, 2020

- Neutron Dipole Moment - April 27, 2020

- Freeman Dyson (1923-2020) - April 20, 2020

- Archival Data Storage - April 13, 2020

- SETI - April 6, 2020

- Larry Tesler (1945-2020) - March 30, 2020

- Power from Raindrops - March 23, 2020

- A Voice from the Crypt - March 19, 2020

- Computer Hashing - March 9, 2020

- Carbon Capture - March 2, 2020

- Knots - February 24, 2020

- When in Rome... - February 17, 2020

- Frigid Legos® - February 10, 2020

- Natural Materials - February 3, 2020

- Martian Atmosphere - January 27, 2020

- Whiskey - January 20, 2020

- An Elastocaloric Calorimeter - January 13, 2020

- Elastocaloric Effect - January 6, 2020

### Deep Archive

Deep Archive 2006-2008

**Blog Article Directory on a Single Page**