CLIL lesson about the relationship between maths and literature

1. Mathematics and Literature

2. Aims
•promoting integration between the
scientific and linguistic disciplines.
Outcomes
•Knowledge : learning some mathematical
principles.
•Evaluation: the relation between scientific
and linguistic subjects.

3. Topic
• Reading of some
extracts of the following
literary text (1992):
“Miss Smilla’s feeling for
snow”
"Il senso di Smilla per la
neve "
by Peter Hoeg.

4. Author and story
• Story
Smilla Quavigaad Jaspersen is the book’s
protagonist. She is 37 and she was born
in Greenland, but she lives in
Copenhagen. She studies glaciology and
she likes maths.
Her favourite friend is a child, Esajas, who
was born in Greenland. He also lives in
Copenhagen, in the same building as
Smilla. His father died and his mother is
unemployed and alcoholic and she does
not take care of him.
Smilla often spends her free time with Esajas
and she reads him a lot of maths books,
such as « Euclide’s Elements».
The sudden death of the child, apparently
accidental, rouses Smilla’s suspicions.
She looks for hidden clues and tracks and at
the end she will be able to find out the
mistery of Esajas’s death.
Peter Hoeg
He was born in Copenhagen,
Denmark in 1957. Before being a
writer, he worked as a sailor, ballet
dancer and actor; these previous
experiences will help him in the
writing of his novels. He received a
Master of Arts in Literature from
the University of Copenhagen in
1984.

5. Read an extract of the book
The only thing that makes me truly happy is mathematics, snow, ice,
numbers. To me the number system is like human life. First you have the
natural numbers, the ones that are whole and positive like the numbers of
a small child. But human consciousness expands and the child discovers
longing. Do you know the mathematical expression for longing? Negative
numbers. The formalization of the feeling that you are missing something.
Then the child discovers the in between spaces, between stones, between
people, between numbers and that produces fractions, but it's like a kind
of madness, because it does not even stop there, it never stops. The
integers plus fractions give rational numbers. But consciousness does not
stop there. He wants to overcome the reason. Adds an operation as absurd
as the square root. He gets irrational numbers. " It 'a kind of madness.
Because the irrational numbers are infinite. They can not be written. They
push the consciousness into the infinite. And by adding irrational
numbers to rational numbers you get real numbers. "

6. It does not end. It never ends. Because now, on the
spot, we expand the real numbers with imaginary
ones, square roots of negative numbers. They are
numbers that we can not envision, numbers that
normal consciousness can not understand. And when
we add the imaginary numbers to the real numbers we
have the complex number system. The first number
system in which it is possible to give a satisfactory
explanation of the formation of ice crystals. It 's like a
big open landscape. Horizons. We approach them and
they continue to move. Greenland is, what I can not do
without! "

7. ANALOGY
THE NUMBER SYSTEM IS LIKE
HUMAN LIFE

11. REAL SET

12. SOLVE THIS PROBLEM!!!!!!!!!

14. IMAGINARY NUMBER SET

15. COMPLEX NUMBERS SET

16. HOMEWORK FOR THE STUDENTS

17. PI :
HISTORY AND CURIOSITY OF A FASCINATING NUMBER
3,1415926535897932384626433832795028841971693993751105820974944592307816406…

18. HISTORY
• The oldest record about this number is « Rhind’s Papyrus»
dated 1650 BC written by an Egyptian scribe, Ahmes.
• In the Bible (VI century BC) there are informations about the
value the Jews used of pi.
• In the third century BC Archimede used this approssimation of
pi=3,14163.
• In 1202 Leonardo Pisano (Fibonacci) used the approssimated
value of pi= 3,141818.
• In later centuries scientists discovered a lot of pi’s digits.
• In the twentieth century then scientists discovered an
increasing number of pi’s digits with the use of computer.
• THE RECORD IS 50 BILLION OF DECIMAL DIGITS

19. WHY DO SCIENTISTS WANT TO KNOW THE
NUMBER OF PI’S DIGITS?
BECAUSE A BETTER KNOWLEDGE OF
THIS MYSTERIOUS NUMBER HELPS
TO UNDERSTAND THE PHYSICS, THE
MATHEMATICS AND GEOMETRY

20. IN 1767 LAMBERT PROVED THAT:
Pi is an
irrational
number
Pi is a
trascendent
number
• It cannot be written
as a fraction
between two
integers
• It is the solution of
any polynomial
equation with
integer coefficients

21. 14th March 14th March 2015
• It is the pi day and it is
celebrated all over the
world.
• On 14th March 2015 the
party was even more
impressive because 3,
14, 15 are the first five
pi’s digits.

22. HOMEWORK FOR THE STUDENTS
• READ THE DIVINE COMMEDY’S
VERSES
PARADISE XIII CANTO 95-101
• TRY TO UNDERSTAND THE MATH’S
PROPERTY WHICH DANTE SPEAKS
ABOUT.

23. RIGHT TRIANGLE INSCRIBED IN A
SEMICIRCLE
• PARADISE: XIII CANTO VERSES 95-101
«Non ho parlato sì che tu non posse
ben veder ch’ el fu re, che chiese senno
acciò che re sufficiente fosse;
non per sapere il numero in che enno
li motor di qua su, o se necesse
con contingente mai necesse fenno;
non si est dare primum motum esse,
o se del mezzo cerchio far si puote
triangol sì ch’ un retto non avesse.»
right triangle.ggb

24. FINAL DISCUSSION
The teacher asks the following questions:
• Can a writer enrich his prose and poetry if he knows the
basic scientific concepts and terminology?
• Can a reader appreciate analogies, metaphors that are
not accessible to those who haven't a scientific culture if
he knows the basic scientific concepts and terminology?
• Can a scientist use a richer language to effectively
expose scientific concepts if he has literary, historical,
philosophical knowledges?