Mathematics and Literature

Aims• promoting integration between the

scientific and linguistic disciplines.

Outcomes• Knowledge : learning some

mathematical principles.• Evaluation: the relation between

scientific and linguistic subjects.

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.

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.

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. "

 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! "

ANALOGY

THE NUMBER SYSTEM IS LIKE HUMAN LIFE

 

 

 

REAL SET

SOLVE THIS PROBLEM!!!!!!!!!

•  

•  

IMAGINARY NUMBER SET

COMPLEX NUMBERS SET•  

HOMEWORK FOR THE STUDENTS

• STUDY ONE OF THE MOST IMPORTANT REAL NUMBERS:

PI:π• IN THE NEXT LESSONS EACH STUDENT

WILL DISCUSS ABOUT HIS OWN WORK WITH THE CLASS.

PI : HISTORY AND CURIOSITY OF A FASCINATING NUMBER

3,1415926535897932384626433832795028841971693993751105820974944592307816406…

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

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

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

CURIOSITY: pi day

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.

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.

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

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?