Why Call It a Witch? // 109

by 7 or 93, then ­ provided you have a big enough sample ­ the same law applies. In fact, Benford's Law is the only scale-invariant frequency law. It is unclear why nature prefers scale-invariant frequencies, but it seems reasonable that the natural world should not be affected by the units in which humans choose to measure it.

Tax collectors use Benford's law to detect fake figures in tax forms, because people who invent fictitious numbers tend to use the same initial digits equally often. Probably because they think

........................................... that's what should happen for genuine figures!

Why Call It a Witch? Maria Agnesi was born in 1718 and died in 1799. She was the daughter of a wealthy silk merchant, Pietro Agnesi (often wrongly said to have been a professor of mathematics at Bologna), and the eldest of his 21 children. Maria was precocious, and published an essay advocating higher education for women when she was nine years old. The essay was actually written by one of her tutors, but she translated it into Latin and delivered it from memory to an academic gathering in the garden of the family home. Her father also arranged for her to debate philosophy in the presence of prominent scholars and public figures. She disliked making a public spectacle of herself and asked her father for permission to become a nun. When he refused, she extracted an agreement that she could attend church whenever she wished, wear simple clothing, and be spared from all public events and entertainments. 110 // Why Call It a Witch?

Maria Gaetana Agnesi.

From that time on, she focused on religion and mathematics. She wrote a book on differential calculus, printed privately around 1740. In 1748 she published her most famous work,

` Instituzioni Analitiche ad Uso Della Gioventu Italiana (`Analytical Institutions for the Use of the Youth of Italy'). In 1750 Pope Benedict XIV invited her to become professor of mathematics at the University of Bologna, and she was officially confirmed in the role, but she never actually attended the university because this would not have been in keeping with her humble lifestyle. As a result, some sources say she was a professor and others say she wasn't. Was she, or wasn't she? Yes.

There is a famous curve, called the `witch of Agnesi', which has the equation

xy2 ¼ a2 ða À xÞ

where a is a constant. The curve looks remarkably unlike a witch ­ it isn't even pointy:

Witch of Agnesi.

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