What is known about Maria Gaetana Agnesi
Maria Gaetana Agnesi was the daughter of a wealthy Milanese patrician, Pietro Agnesi, and was able to study from an early age languages of a broad variety as well as philosophy and fine arts. One entertaining anecdote from her early life is that she knew 7 different languages and was called the “seven tongued orator” by age 11 (Italian, French, Greek, Hebrew, Latin, Spanish, German). In addition to her passion of studying languages and philosophy, she was also indebted to the service of enabling women’s access to the modern sciences and mathematics. Much of her time spent working with philosophy was motivated by this goal. In addition to her interests in philosophy, she also wrote an introductory Calculus book entitled Instituzioni Analitiche for young adults to learn the basics of infinitesimal Calculus that was published in 1748. What is more, her study of mathematics and the subject matter of her book was primarily motivated by her interest in studying analysis for its own sake and geometry rather than its applications to the physical sciences. She was celebrated in her earlier life as an inspiration for other women to study the sciences and mathematics, however, rather surprisingly, as she approached the end of her days, she abandoned the study of mathematics entirely and devoted the rest of her life to the aid of the poor in Milan and social justice. By the latter end of her life in 1783, she had given away all of her possessions and lived as a resident in Pio Albergo Trivulzio until she died in 1799.
What makes the equation interesting and special
The eponymous curve of Maria Agnesi, the subject of this week’s discussion, often entitled the “Witch of Agnesi” interestingly has very little to do with witchcraft of any sort. In fact, this appellation was most likely introduced by a mistranslation of Italian into English and German. The Italian word versiera (from Latin versoria) is actually related to a nautical term for a rope to tie the sails of a ship. This word has a peculiar similarity, however, to the similarly spelled word aversiera (from Latin adversaria “adversary”), that had come to mean “she-devil.”
The curve itself had attracted little attention from mathematicians previously due to its apparent lack of applications to the physical sciences. However, the beauty of the curve lies in its geometric properties. The curve itself may be constructed by creating a circle inside of two lines tangent to two points on opposite ends of the circle. Then a chord may be created from the bottom point of the circle that intersects with the upper tangent line. A second line may be created by drawing a line parallel to the lower tangent line. The point D where these lines intersect then circumscribes the circle. If you create another vertical line that intersects the upper point on the tangent line C, then the point E that intersects the parallel line on the circle is the value of the “Witch” as you circumscribe the circle with D.