Panorea: first attempt
On Friday 27th November 2009 was my first attempt to lead the group of the studio of choreography. It was the first time that I had to teach math stuff to a group of actors, dancers and choreographers all of whom were adults. It was difficult and challenging at the same time to explain my strong feeling by then – and belief at the moment – that mathematics share a lot in common with representing and creative arts. I had almost one hour and a half to practice with them. I divided my session into two parts. First we dived into the mystery of prime numbers and we investigated one of their most important properties and secondly we played with divisibility of natural numbers. For each idea first I made a short theoretical introduction and afterwards the group practiced on the related excercises.

A] Investigating natural numbers (properties & functions)

A set is any collection of numbers that belong to a defined category.

A set can be finite (e.g. the set of hours in a day) or infinite (e.g. the set of hours in the future).

Natural numbers - also called positive integers - are the set of numbers from 0 on obtained by adding 1 first to 0, and the sequence to each number so obtained, thus : 0,1,2,3,4,5,...

(the three ellipsis points “…” indicate and so on to infinity).

Natural numbers have beginning (0) but no end: there is no last natural number.

Each natural number n has an immediate successor n+1.

1st classification of natural numbers: even & odd is given by the division by 2

• Even numbers are those divisible by 2

• Odd numbers are those that are not divisible by 2.

The steady alternation of even and odd marks the sequence of natural numbers

Even are doubles (2n)

Odds (2n+1)

2nd classification of natural numbers: prime numbers

Prime numbers are the numbers that are the product of themselves and 1 – they cannot be divided except by themselves and 1. This group includes numbers 2, 3, 5, 7, 11, 13, 17 and an infinite list of others. Every integer is either a prime, or the product of prime numbers. To identify a number by its primes is called “decomposition into prime factors”.

Each number has one and only one formula of decomposition into prime factors – unique to it – a fact of great importance. Since every decomposition is unique, the collection of its prime divisors can be considered its signature e.g. 30107 = 7 x 11 x 17 x 23.

Exercise

First we choose a few numbers. Secondly, we decompose them into their prime factors. Then each person represents a prime number. And every time I show them one of the numbers we have chosen , the corresponding primes try to build up the given number.

I tried this exercise with 4 persons. Each one represented one of the first four prime numbers, thus the first was 2, the second represented 3, etc. I had already done the decomposition into prime factors for numbers which were the product of 2,3,5 and/ or 7.

We tried to build up, or - preferably to me - to construct the signature - of the following numbers: 210=2x3x5x7, 60=22x3x5, 20=22x5, 150=2x3x52, 300=22x3x52.

Is the signature something still or there is movement that is being born? What happens when a prime number is in power 2? Which is the difference between 2 and 22 in a signature? How this affects the shape or the movement of the prime? Which is the feeling or the meaning of being a number and a part of another number at the same time? Which is the difference between a prime number alone and a prime number as a factor in a decomposition into primes’ product?

Πανωρέα / Πώς ξεκίνησα.

INVESTIGATING MATHS APPLIED IN PERFORMING ARTS

I am a Mathematician, working at the moment as a home tutor, a teacher in private schools and a researcher of Biomedical Engineering in NTUA (National Technical University of Athens). At the same time I undertake dance classes at “KINITIRAS Studio”. During my studies both in maths and in biomedical engineering I have also taken part in drama classes and seminars.

I have always known that I loved both mathematics and performing arts and from my experience in both fields I find the way they work very analogous. My dream is to find a way to bring these ostensibly different worlds closer one to each other and find a balance between them.

Last summer I came along for the first time with the idea of investigating the relations and the sections between mathematics and dance as well as theatre. The idea came up while I was reading Michael’ s Chekhof book “TO THE ACTOR on the technique of acting”. Being a mathematician and – above all – a teacher, I realized the existence of many similarities between the way an actor and a student (who studies mathematics) is being educated. After finishing this book, I started searching about any kind of information related to mathematics applied in performing arts. By today this research revealed me a very interesting field which has been poorly investigated (especially in Greece); so it was a beautiful surprise when last October I saw the announcement of the research choreography project on “KINITIRAS studio” website.

Here follows a brief description of my first and non processed ideas towards “Mathematics in Performing Arts”:

1. Lending creativity through Geometry. Basic geometrical structures, simple laws and theorems can warm up our imagination and make things happen on stage.

2. Similar characteristics between conceiving, constructing and organizing a) a mathematical proof and b) a performance .

3. A unity’s or group’s physical and emotional movement in space leaded by algebraic theories and rules.

My idea has as a double purpose: firstly to find performing ways to convey mathematics and maybe make them less daunting both to the performers and to the public and secondly to look for new ways to create theatrical experiences or to let choreographic pieces happen.

From the begining of this procedure I enjoyed being part of a research group and sharing my ideas with people who are also interested in this investigating procedure.

Finally, I find totally necessary and useful a dialogue on all these theories with professionals and experienced people in performing arts.

Panorea Baka

Αγγελική / Πώς ξεκίνησα.

To στούντιο χορογραφίας το είδα σαν αφορμή ή ελπίδα ώστε κάποιες σποραδικές και χαοτικές σκέψεις μου να μπούνε σε μία τάξη. Τάξη με την έννοια της εφαρμογής, γιατί δεν είναι και εύκολο να μετατρέψεις το χάος σε τάξη... Με τις σπουδές μου στο φυσικό πήρα ερεθίσματα από την ειδική θεωρία της σχετικότητας, τον ηλεκτρομαγνητισμό κ.α. που τροφοδότησαν την φαντασία μου περισσότερο παρά τις γνώσεις μου. Έχοντας και πτυχίο χορού σκέφτηκα μήπως ήρθε η ώρα να μπει σε εφαρμογή όλη αυτή η φαντασία. Ίσως έτσι σταματήσω να ονειροπολώ και αρχίσω κι εγώ να ζω σε αυτή τη ζωή μαζί σας..

Μαριάννα / Πως ξεκίνησα.

I think I just want to play, to explore, to find out what I want to do, what I like, what I can give, what I can share; then I am thinking, what else more than that

Τo be as you are, to find out who you are through your movement.

To express yourself without speaking, to express yourself and do not worry for the meaning. To be interested for what is happening now, to be interested to live this unique moment of movement, you do not miss anything you do not have to worry for anything.

To not feel alone, to feel that you can coexist with others, that there are others who share this moment with you, not because you like them, not because they know you, just because you can feel the movement of another living being, just because the others can feel your movement.

To not worry for the conclusions.

You can just live, you can just move, life anyway is confirmed by the movement.