Activity

Drawing an irrational number

Characters:

Theano of Crotone

Theme: Irrational numbers (rational and irrational numbers)

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 > 4th(A) ESO > Number sense

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

Spain > Mathematics > 4th(B) ESO > Number sense

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

Enunciation

The golden number might have been the first irrational number known to the Greeks. When the Pythagoreans discovered that irrational numbers existed, i.e. that they could not be written as the quotient of two whole numbers, they were dismayed, as this fact broke many of their philosophical theories. That is why they decided to keep this discovery a secret.
Theano of Crotone, a Pythagorean mathematician, was the first woman to carry out these divisions, confirming thus the existence of irrational numbers. As a good Pythagorean, she believed and defended that all material objects were composed of natural numbers, so that the measure of anything could be expressed with an exact measure. However, she was also the first to posit the existence of the golden ratio as the essence of the universe.
The golden number, or golden ratio, is represented with the Greek letter &Phi; (Phi), honouring Phidias.
She drew the distance of Phi on the number line from the construction below:
<a title="Construcci&oacute;n con regla y comp&aacute;s de Phi" href="http://inclusion.womenslegacyproject.eu/uploads/resume/attachment/1665/Imagen_1.png" target="_blank" rel="noopener"><img title="Construcci&oacute;n con regla y comp&aacute;s de Phi" src="http://inclusion.womenslegacyproject.eu/uploads/resume/attachment/1665/Imagen_1.png" alt="Construcci&oacute;n con regla y comp&aacute;s de Phi" width="694" height="264" /></a>
Demonstrate the existence of the square root of two by drawing it on the number line.&nbsp;

Observations and context

- Crotone was in Theano's time a colony of Magna Graecia.

- Enheduanna (25th century BC) was a predecessor of Theano of Crotone, considered the first recorded woman in the history of science and the first to sign her works, in cuneiform script .

- Some of Theano's contemporaries are other women in the Pythagorean school that were born around 500 BC, such as Damo, Myia and Arignote of Crotone, considered to be daughters of Theano and Pythagoras by several authors. Even though there is not much information about them, some other women belonging to this group were Babelica of Argos, Beo of Argos, Quilonis, Echecrates of Phlius, Ecellus and Ocellus Lucanus, Habrotelia of Tarento, Cleecma, Cratesiclea, Lastenia of Arcadia, Pisirroda of Tarento, Filtis, Teadusa, Timica and Tirsenis of Sibaris.

- After Theano we can mention Aglaonice, or Aganice of Thessaly, (3rd century BC, known for her ability to predict eclipses) and Hypatia (4th century AD).

Description

Representing irrational numbers in a number line through the Pythagoras theorem.

Drawing an irrational number

Enunciation

Observations and context

Description

Answer

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