Activity

The oranges

Characters:

Maria Gaetana Agnesi

Theme: Functions applications

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

Enunciation

<img title="Women's Legacy logo" src="//inclusion.womenslegacyproject.eu/images/LogoWL.svg" /><hr /><img title="Maria Gaetana Agnesi" src="//inclusion.womenslegacyproject.eu/uploads/resume/attachment/2732/MariaGaetanaAgnesi.jpg" alt="Maria Gaetana Agnesi" width="200" height="233" />
Maria Gaetana Agnesi, Italian mathematician of the 18th century, well known for the "Agnesi curve", is recognized mainly in the area of analysis, with the publication of the first complete book of Differential and Integral Calculus.
Solve the following problem from the area of analysis, in which Maria Gaetana Agnesi worked so hard:
Maria Gaetana Agnesi went to the market to buy some oranges. There, she read a chart with the price she had to pay depending on how many kilos of oranges she bought.
<table style="border-collapse: collapse; width: 62.7666%;" border="1">
<tbody>
<tr>
<td style="width: 12.523%;">kg of oranges</td>
<td style="width: 12.523%; text-align: center;">0</td>
<td style="width: 12.523%; text-align: center;">1</td>
<td style="width: 12.523%; text-align: center;">2</td>
<td style="width: 12.523%; text-align: center;">3</td>
<td style="width: 12.523%; text-align: center;">4</td>
<td style="width: 12.523%; text-align: center;">5</td>
<td style="width: 12.523%; text-align: center;">6</td>
</tr>
<tr>
<td style="width: 12.523%;">Price (in euros)</td>
<td style="width: 12.523%; text-align: center;">0</td>
<td style="width: 12.523%; text-align: center;">2</td>
<td style="width: 12.523%; text-align: center;">&nbsp;</td>
<td style="width: 12.523%; text-align: center;">&nbsp;</td>
<td style="width: 12.523%; text-align: center;">&nbsp;</td>
<td style="width: 12.523%; text-align: center;">10</td>
<td style="width: 12.523%; text-align: center;">&nbsp;</td>
</tr>
</tbody>
</table>
a) Indicate which quantities are the independent variable and the dependent variable.
b) Complete the chart.
c) Express the data as ordered pairs and represent them graphically.
d) What do points (0,0); (1,2) and (5,10) mean?
e) Does it make any sense to connect the points in the graph? Why?

Observations and context

- Maria Gaetana Agnesi was a child prodigy that, from a very young age, was able to communicate in several languages and to have deep philosophical and scientific conversations. Her sister, Maria Teresa Agnesi, was a musician and composer.

- 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

A simple problem is set out that can be solved through the study of a function. Some basic concepts on functions are studied and its graph is represented.

The oranges

Enunciation

Observations and context

Description

Answer

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