Activity

Studying the curve (the witch) of Agnesi

Characters:

Maria Gaetana Agnesi

Theme: Representation of functions. Graphs.

Competencies

Mathematical competence in science, technology and engineering

Personal, social and learning to learn competence

Competence in cultural awareness and expressions

Subjects and year by Educational System

Spain > Mathematics > 1st ESO > Algebraic sense

Spain > Mathematics > 1st ESO > Socio-affective sense

Spain > Mathematics > 2nd ESO > Algebraic sense

Spain > Mathematics > 2nd ESO > Socio-affective sense

Enunciation

Maria Gaetana Agnesi was a famous 18th-century mathematician who published the first complete book on calculus. In that book, there were &nbsp;graphs such as the following ones:
<img title="Agnesi curve 1" src="http://inclusion.womenslegacyproject.eu/uploads/resume/attachment/2734/Agnesi_1.jpg" alt="" width="500" height="469" />
<img title="Agnesi curve 2" src="http://inclusion.womenslegacyproject.eu/uploads/resume/attachment/2735/Agnesi_2.jpg" alt="Agnesi curve 2" width="800" height="249" />
1. &nbsp; &nbsp;Look at the following images. Do you think they represent the same function?&nbsp;
2. &nbsp; &nbsp;Now, you will study them in depth by comparing each one thoroughly.&nbsp;
<ol style="list-style-type: lower-alpha;">
<li>For which value of X does the first function reach its maximum? And the second one? Do they coincide?</li>
<li>When x=5, what is the value of the first function? And the second one? Do they coincide?&nbsp;</li>
<li>When x=10, what is the value of the first function? And the second one? Do they coincide?</li>
<li>When x=20, what is the value of the first function? And the second one? Do they coincide?</li>
<li>When x= -5, what is the value of the first function? And the second one? Do they coincide?</li>
<li>When x= -10, what is the value of the first function? And the second one? Do they coincide?</li>
<li>Now choose a different value for x and check if it is the same when applying the first function and the second one.</li>
</ol>
3. &nbsp; &nbsp;After studying them in depth, what are your thoughts? Do they represent the same function or not? Why do you think they have a different graph? What is happening? Do you think there's more than meets the eye?

Observations and context

- Alternatively, we can tell students how this curve was mistranslated as "the witch of Agnesi" instead of "Agnesi’s curve" and explore what connotations or motivations there could be behind that mistranslation (by a man) of one of the best texts on mathematics at the time, written by a woman.

- Some of Maria Gaetana Agnesi's forerunners in mathematics, philosophy and astronomy are Theano of Crotone (c. 546 BC - c. 450 BC), Hypatia of Alexandria (c. 370 – c. 416) and, in the early modern period, Sophia Brahe (1556-1643), Maria Cunitz (1610-1664), and Elena Lucrezia Cornaro Piscopia (1646 -1684).

- Some of her contemporaries were renowned scientists such as Margaretha Kirch (1703-1744), astronomer; Faustina Pignatelli Carafa (1705-1785), physicist and mathematician; Émilie du Châtelet (1706-1749), mathematician, physicist and philosopher; Laura Maria Catharina Bassi (1711-1778), scientist, poet, and philosopher; Angelique-Marguerite le Boursier du Coudray (1712-1794), midwife; Dorothea Christiane Leporin (1715-1762), doctor; Anna Morandi Manzolini (1716-1774), anatomist; Marie-Geneviève-Charlotte Thiroux d’Arconville (1720-1805), chemist, anatomist, and biologist; María Juana Rosa Andresa Casamayor de la Coma (1720-1780), mathematician; Nicole-Reine de la Brière Lepaute (1723-1788), astronomer; Marie Anne Victoire Pigeon (1724-1767), mathematician, or Maria Angela Ardinghelli (1728-1825), mathematician and physicist, among others.

- Other relevant scientists in the 18th century were Maria Christina Bruhn (1732-1808), chemist and inventor; Claudine Picardet (1735-1820), chemist, mineralogist and meteorologist; Jeanne Baret (1740-1807), botanist and explorer; Caroline Lucrecia Herschel (1750-1848), astronomer; Marie-Anne Pierrette Paulze (1758-1836), chemist; and Sophie Germain (1776-1831), mathematician and physicist.

Description

In this activity students will be shown two graphs of the same witch of Agnesi. Students will learn how both graphs are the same, even if they are represented differently. They will also work on mistakes and detecting fallacies.

Studying the curve (the witch) of Agnesi

Enunciation

Observations and context

Description

Answer

Documents

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