These are actual student papers that were not designed to be web pages. They may contain historical, grammatical, mathematical, or formatting errors. These papers were graded using the criterion mentioned in the paper directions, and the writing checklist. The test review sheets and the WebCT tests are good indicators of the mathematics that was discussed in class during and/or after each presentation.
Maria Gaetana Agnesi was one of the most important figures in the 18th century. Around this time in Italy, where the Renaissance had its origin, women were making their mark in the academic world. Women of intellect were admired by men and were never mistreated for being educated or intellectual. This enabled women to do things that they would've never thought possible before, such as working with mathematics, medicine, literature, and participating in the arts. This attitude also opened the door for Maria. Agnesi and changed the way we look at mathematics.
Maria Agnesi was born in Milan, Italy, on May 16, 1718. She was the eldest of 21 children delivered by three successive wives of Pietro Agnesi, son of a wealthy silk merchant. Pietro was a professor of mathematics and provided his daughter with an excellent private education. "She was recognized as a child of prodigy very early; spoke French by the age of five; and had mastered Latin, Greek, Hebrew, and several modern languages by the age of nine." [Osen, 40] This earned her the appellation "Oracle of Seven Languages".
In 1738, at the age of twenty, she wrote, Proposition Philosophicae, a collection of essays on philosophy and natural science based on the discussions of the intellectuals who gathered at her father's home and the inspiration of Isaac Newton. In many of these essays, she talked about how strongly she believed that women should be educated. Shortly following that she began working on her most important work, Analytical Institutions. When this book was published, a great deal of excitement struck the academic world because it was the first and most complete works on finite and infinitesimal analysis. The first section of the book was dedicated to the analysis of finite quantities, and elementary problems of maxima, minima, tangents, and inflection points. The second section deals with the analysis of infinitely small quantities and the third about integral calculus. Finally, the last section talks about the inverse method of tangents and differential equations. This was originally designed as a textbook for her younger brothers.
After the success of her book, on the nomination of Pope Benedict XIV, Maria was elected into the Bologna Academy of Science. Her name was added to the faculty roll and the university sent her diploma dated October 5, 1750. However, there is a debate on whether or not Maria excepted this position. It is known that when Agnesi's father became ill in 1748, she lectured in his place, but there is controversy if she accepted the
Her behavior implies that she was not dedicated to mathematics, which more than likely explains why she gave it up after her father's death. It seems as if her father was her inspiration for her interests in mathematics. Many historians debate on whether or not she was truly dedicated. What we've implied is that the book that she wrote was meant to educate her brothers, not for the public's use. The fact that she gave it up when her father passed on, leaves us to believe that she was not willing to spend the rest of her life doing mathematics. Instead, she devoted the rest of her life to religious studies and charitable works. She died before her 81st birthday in May 1799, but her contribution to math made it possible to clearly integrate the knowledge of calculus.
The solution that she is remembered for is called "the witch of Agnesi". This name was not given to this curve because she was a witch. The word witch originated from the word "versiera", which meant to turn in Latin. It so happened that a similar sounding Italian word "avversiera" appears in the English translation by Reverend John Colson. This translation error was made when Analytical Institutions was being converted from Italian to English. Historians believe that Colson simply looked into an Italian-English dictionary and found "versiera" translated as "witch". Even though this slip-up seems like a bad thing, it is what she is most popular for because the title of the curve stands out.
Now that we know what the Witch of Agnesi is, let’s try to explain how we graph
it, and what it means. Throughout the sources on the versiera, there are several
ways to generate the graph and the equations.
The algebraic expression that generates the curve is
where a is the diameter of the circle, or the height of the curve.
We then need to take the inverse of the expression because Maria Agnesi used the x-axis as the vertical axis and the y-axis as the horizontal.
For the example shown, a=1,2,3