What would you do: If you woke up and your math homework was miraculously completed? If you could speak more than five different languages? If your parents’ wishes differed from your personal interests and goals?

Maria Gaetana Agnesi Mathematical Heron

18 th Century Women Women educated in convents –Learn to read & write –Focus on dressmaking & social graces Some Women held jobs as university positions as assistants during Enlightenment Priority to take care of the family and home

Early Years B orn on May 16, 1718 in Milan, Italy to a wealthy family. She displayed great intelligence from an early age, especially in learning languages. Her father, a mathematics professor, recognized this and encouraged her to develop these talents.

Education Father Knows Best –Academic gatherings with Scholarly guests –Converse about academics in guest’s native language –Private tutor for Maria Late night studying - Somnambulist- wake up to find she had solved a problem in her sleep Agnesi asked to attend Convent because of her introverted personality but her father would not allow

Achievements At 20, she wrote Propositiones philosophicae, a work discussing mathematics, mechanics, logic, chemistry, zoology, and more At 30 years, she published her renowned work Analytical Institutions, a book including elementary and mathematical ideas from arithmetic and trigonometry to calculus and differential equations. One of the first books to be written for younger audience as an educational resource

Achievements Served as replacement mother to 20 siblings, created Institutions to teacher her brothers Named honorary member by Pope Benedict XVI and eventually chair of department at University of Bologna Best known for her work with a family of curves known as “The Witch of Agnesi”

Later Years Lectured under her father for several years during his illness When her father died in 1752 her passion for math and science faded From then on she devoted her life to charitable and religious works Died in1799 and is buried with the poor at her request

Witch of Agnesi Previously studied by Fermat and later by James Gregory “Witch” is a mistranslation of a word meaning cubic curve View moveable applet to see how the function is created.

Witch of Agnesi Consider the circle with diameter PQ and center at (0, a) as shown. A tangent line L1 is constructed to the circle at point Q. A line from point P is drawn to intersect the circle at point R and extended to intersect line L1 at point S. From point S a line is drawn parallel to the y-axis, intersecting L2 at point W. Agnesi’s curve is the set of points W generated by points R on the circle. - From Sanerson & Smith p. 110 S W R L1 L2 (0,2) P Q,