Activity

The sacks

Characters:

Elena Lucrezia Cornaro Piscopia

Theme: Strategies for deducing reasonable conclusions from a mathematical model.

Competencies

Competence in Linguistic Communication

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 > 4th(B) ESO > Algebraic sense

Spain > Mathematics > 4th(B) ESO > Socio-affective sense

Enunciation

<img title="Women's Legacy logo" src="//inclusion.womenslegacyproject.eu/images/LogoWL.svg" /><hr /><img title="Elena Lucrezia Cornaro Piscopia" src="//inclusion.womenslegacyproject.eu/uploads/resume/attachment/3912/Elena_Lucrezia_Cornaro_Piscopia.png" alt="The image depicts a full-colour portrait of Elena Lucrezia Cornaro Piscopia." width="78" height="95" />
Elena Lucrezia Cornaro Piscopia, a 17th-century Venetian philosopher and mathematician, was the first woman to obtain a PhD. At this time, Italian society was passionate about debates on philosophy and mathematics, considered inseparable branches of knowledge. Mathematical logic problems are a clear example.
The following problem of mathematical logic is proposed.
We have 10 sacks with 100 balls each. All the balls weigh 10 g, except those in one of the bags, in which they all weigh 9 g.
Reason how you can find out which is the different bag using the scales only once.

Observations and context

- The proposed activity can be adapted to different levels. Only the number of available bags should be increased to make the problem more complex.

- It is important to check the solution.

- Elena Cornaro Piscopia was an esteemed member of various academies throughout Europe and received visits from scholars from all over the world. She liked to debate and lecture on theology and compose music. Even today, she is widely cited by scholars and writers.

Although she mastered almost all branches of knowledge, she taught mathematics to students from all over Europe at the University of Padua.

In her time, Italy was more advanced than the rest of Europe and there were already women studying science and mathematics at the University, but access to a doctorate was still forbidden to them. When she was not allowed to study for a doctorate in Theology, since she ran into the intransigence of the Church that could not conceive of a woman teaching monks, she decided to prepare for a doctorate in Philosophy.

- Predecessors of Piscopia are Theano of Crotone (c. 546 – c. 450 BC) and Hypatia of Alexandria (c. 370 - c. 416 AD), who were also mathematicians and philosophers; Sophia Brahe (1555-1643), astronomer, horticulturist, alchemist and genealogist.

- Her contemporaries were renowned astronomers, such as Elisabeth Hevelius (1647-1693); Jeanne Dumée (1660-1706); Margaret Flamsteed (1670-1730); Maria Margarethe Winckelmann Kirch (1670-1720) or Maria Clara Eimmart (1776-1707); and important scientists, such as Maria Sibylla Merian (1647-1717), naturalist, entomologist, and scientific illustrator; and the mathematician Marie Crous.

Description

The goal is to find the solution to a problem by applying logic. To do this, it is necessary to organize the information and find the strategy that leads to the solution, fulfilling the conditions imposed on it. It is important to check the result.

Answer

Documents

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