Bharatanatym is an ancient Indian dance form that has a significant mathematical and rhythmic component to it. I have been learning, mastering and performing this type of dance since I was four years old. The word Bharatanatym comes from Sanskrit where ‘bha’ means expression, ‘ra’ /music, ‘tha’ /rhythm and ‘natya’/dance.  The dance form combines rhythmic dance steps called aduvus with storytelling from Indian mythology. The steps are incredibly structured with exact body positions and body angles. The body positions, arm angles and hand gestures are all codified. Stories that illustrate stories of Hinduism like the Ramanayam are articulated through this form of dance. 

 

The adavus are based on the number of beats in a specific rhythm in a particular Carnatic music piece. The adavus are taught with increasing difficulty starting with steps that are multiples of 2 then 3 and so on. The aduvus are permutations and combinations of rhythmic sets of 3 to 9 beats. When a song has 7 beats, different adavus of 3 and 4 are combined.  If a song has 35 beats, you could have combinations of sets of 3 and 4 repeated 5 times or steps with 6 and 8 repeated twice and then adding a step with 7 beats. All of this math is done instinctively by a bharatanatyam choreographer. What looks like art and expression on stage is a series of intricate combinations of math permutations. Like Plato said ‘I would teach children music, physics, philosophy; but most importantly music, for the patterns in music and all the arts are the keys to learning.’

 

In bharatanatyam the hand positions are called mudras. There are about 32 mudras with one hand and 23 that require two hands. The mudras are used to communicate specific creatures, emotions, actions or events. They help the dancer convey the story they are trying to express. They are often deeply connected to human emotions. Scientists in Maharashtra, India used hypercomplex representations, the quaternion Fourier transform, to study mudra images. They compared mudra meanings with the calculated features. These features included area, major axis length, minor axis length, centroid and eccentricity. The images of the hands were captured with various camera angles. They were able to train the database to recognize mudras which can then be used for gesture recognition and possibly interpretation of emotion. This type of recognition can be used in AI and robotics to further understand human emotion. 

 

Furthermore, Bharatanatym has 3 basic body positions: araimandi (half-sitting position), muzhumandi (full sitting position) and samapadam (standing position). Each of these positions require balance, strength and grace. The muscle positions and equilibrium required is highly scientific and done in such a way not to injure the knees and ankles. The physiology of the specific positions require the dancer to have strong quadriceps and hamstrings. The positions require symmetry in positions and involve many triangles for balance and strength. In the turning movements, centripetal force is used to maintain stage position and balance. There are precise angles that the body is held in to help with balance and strength often creating 45 degree angles. These body positions are deeply rooted in math.  

 

Because of the exact body positions and movements, Bharatanatyam has been used to teach math to students, specifically geometry. Dr. Iyengar used dance to teach geometrical shapes and patterns by understanding body positions. The theory was that math as a subject is often thought to be either easy or hard by students. But, by incorporating dance, math could be taught to students who are different kinds of learners: visual/spatial, body/kinesthetic, or musical and rhythmical. It became clear in her study that students appreciated incorporating dance into math. They were able to visualize congruence, shapes, symmetry and angles through body positions. Silambam Houston has a youtube series called dancing into STEM where math concepts like gravity, the water cycle and metamorphosis are studied through Bharatanatym and various adavus. This integration of the arts, math, and sciences is something that can help non-traditional learners become contributors and make discoveries in the field. 

 

Math is deeply integrated into music and dance. In Bharatanatyam, math can be seen throughout the rhythm, foot work, body positions and beats. Further analysis of the footwork and sounds emanating from the use of just the toes, just the heels or the whole foot would be interesting to study. The way the sound travels from the footwork and the specific steps could also be studied. The mathematical phenomenon called ‘Fourier Transform’ could help us analyze the footwork and the sound that’s produced. It shows that any waveform can be written as a sum of sinusoidal functions. The initial computations done before computer algorithms were inefficient and cumbersome. But with the advent of algorithms the Fourier Transform has impacted so many different fields. By understanding the fast fourier transform, computers were able to take numbers to create sound. This change from tape to digital sound gave engineers an ability to modify and make changes to composition without automatically affecting tempo and pitch. The use of a Fourier series to study periodic functions allowed sound engineers to analyze sounds and eventually synthesize them. This impacted speech enhancement, digital music creation and technologies enabling wireless audio networking. The use of Fourier analysis also helped create time-frequency scattering which has transformed new possibilities for texture synthesis. This intersection of dance, art, math and sound will continue to transform and create new and exciting disciplines of music and dance that will engage and inspire future generations of artists. 

 

 

Recognizing Bharatnatyam Murray Using Principles of Gesture Recognition, Mozarkar, Sowetan, Warnekar Dr. C.S. IJCSN International Journal of Computer Science and Network Volume 2, Issue 4, August 2013 

 

Bharatanatyam and Mathematics: Teaching Geometry Through Dance, Iyengar Mukunde Kalpana  Journal of Fine and Studio Art vol. 5(2), pp. 6-17, October 2015 Academic Journals

 

Bharatanatyam: Art, Science and Maths Mitali Maharaj Sept 14, 2020 bemitalimaharaj.worldpress.com

 

Postural analysis in female Bharatanatyam dancers: a cross-sectional study, Panhale, Vrushali P., Walankar, Prachita P., Sridhar, Aishwarya Panhale et al Bulletin of Faculty of Physical Therapy 2021 2

 

Fourier at the heart of computer music: From harmonic sounds to texture Vincent Lostanlen, Joakim Anden, Matheiu  C.R. Physique 20 (2019) 461-473