Mainly during 2012 the tiny research was made. I was searching for a way to engage mathematical thinking into the dance creating process. I wished to combine math and dance in one work, to bring the intelligence in dance, to utilize mathematical tools for making a dance material, to connect in some curious, not obvious way dance and mathematics.

I received academic higher education in mathematics and have professional experience in contemporary dance. The idea of connecting dance and mathematics sprung to my mind after participating at AND_Lab, which is an artistic research and scientific creativity laboratory, produced by RE.AL and directed by João Fiadeiro and Fernanda Eugénio.

Olga Sevostianova, my colleague, a professional contemporary dancer from Yekaterinburg as well, strongly supported the research. We were experimenting a lot together, and eventually co-created dance performance “Algorithms. Anamorphoses. Anomalies.”

**Some links**

In the beginning, I would like to mention some of materials that I found on the theme “Dance and Mathematics” on the Net: How do dance and math relate, Math Dance, INTEGRATION WITH DANCE/MATHEMATICS, Quick-sort with Hungarian (Küküllőmenti legényes) folk dance, Handlebars Math Dance.

**Sets of movements**

Now I will describe my own discoveries. The research was narrowed to the set theory, very basic in mathematics. In my particular situation, I considered sets of movements.

*Set theory** is the branch of mathematics that studies general properties of sets. Set theory lies in the basis of the majority of mathematical disciplines; it had a profound influence on understanding of the subject of mathematics itself.*

*Set** is a collection of well defined and distinct objects.*

The created set of movements is a sequence. Power of the set is N+1.

*Sequence** is an ordered list of objects. The same elements can appear multiple times at different positions in the sequence.*

*Power of set** (or cardinal number) for a finite set is a natural number which is the number of elements in the set.*

**Dance and Math Laboratory at BIDE 2012**

I participated at the Barcelona International Dance Exchange in April 2012 and facilitated a laboratory there. The lab was devoted to the theme “Dance and Mathematics.” I worked with the group of professional dancers from different countries, introduced to them the above described way of creating sets of movements and making simple transformations of the set and how this can be described in set theory/math terminology. We created one set of movements using accumulation and did transformations (inversion and symmetrical right-left transformation) of the set, then performed different combinations of the transformations in groups like we did above in duet, we extended this to quartet.

That was a whole day laboratory, therefore after lunch we could develop in some way the material that we learned in the morning. Below I’ll describe what we presented at our showing in the evening.

*A set A is a **subset** of a set B if A is “contained” inside B. A and B may coincide.*

We used “*igrek*” instead of “*gamma*“, and named loudly all the movements using our terminology to have better understanding of what we are doing and to use a common special language that we know and understand in the group. We started in the circle and then gradually could move through space. Using the occasion, I wish to mention and thank the participants of the workshop: Laura Jantunen, Danai Pappa, Yung Huai Huang, Ya Chun Yang, and Pipaluk Supernova. The link on video from our showing is here.

**Some of hypotheses**

I have described some of the material which was tested in practice, now I would like to share some of my hypotheses.

**First**, I would mention about a possible **algorithm of creating a more complicated math-based dance material**. You have to follow three steps:

(1) Using an iterative algorithm *create a dance sequence*.

Preferably invent Your formula here. Be precise and accurate while You create Your dance sequence using the formula.

(2) Add or subtract any movement inside the sequence, between the movements. It would be an easy change: *Addition and subtraction ±*

(3) Now apply any *transformation* to any part of the sequence, any function is possible here. It would be great to make the dance phrase more colorful at this step: add some details inside, to the already existing movements; some nuances, may be traveling in space. Everything is possible, so use your creativity and artistic approach here.

**Second**, I have one more hypothesis. While we get several sets of movements, we can operate with the sets: unite them, intersect and subtract. Thus, **set operations** may be possible to consider.