![Page 1: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/1.jpg)
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?
![Page 2: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/2.jpg)
Maria Gaetana Agnesi
Mathematical Heron
![Page 3: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/3.jpg)
18th 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
![Page 4: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/4.jpg)
Early Years
Born 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.
![Page 5: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/5.jpg)
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
![Page 6: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/6.jpg)
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
![Page 7: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/7.jpg)
![Page 8: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/8.jpg)
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”
![Page 9: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/9.jpg)
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
![Page 10: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/10.jpg)
Witch of Agnesi
• Previously studied by Fermat and later by James Gregory• “Witch” is a mistranslation of a word meaning cubic curve• http://www.compasstech.com.au/ARNOLD/geogebra/witch.html
View moveable applet to see how the function is created.
![Page 11: 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’](https://reader036.vdocument.in/reader036/viewer/2022072016/56649ef65503460f94c098c1/html5/thumbnails/11.jpg)
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
,