Geometric Analysis of Ballet Path Based on Least Squares Method
DOI:
https://doi.org/10.54097/fw55eh77Keywords:
Ballet, Dance Path Analysis, Geometry, Least SquaresAbstract
Mathematics and ballet are unrelated seemingly, but a closer look reveals profound similarities between them. Both are based on precision and strict control, and ballet movement gestures and mathematical equations demonstrate rigorous geometric design and systematic mechanisms together. This study aims to explore how geometric methods can be used to optimise the movement and step paths in ballet, thereby enhancing the symmetry and aesthetics of the dance. By applying combinatorial mathematics and geometry, this study analysed the movement arrangements and paths of the Bluebird choreography, using least squares to fit geometric shapes (e.g. squares, circles, ellipses and triangles) to optimise the dance movements. In the experiment, the dance movements were recorded and analysed using advanced mathematical modelling and motion capture techniques to measure the error between the geometric shapes and the actual dance movements. The results of the study showed that mathematical optimisation significantly enhanced the beauty and expressiveness of the dance choreography. This study revealed the mathematical aesthetics in the art of dance and provided a new perspective for future choreography.
References
[1] Watson A. Dance and mathematics: Engaging senses in learning[J]. Australian senior mathematics journal, 2005, 19(1): 16-23.
[2] Belcastro, Schaffer K. Dancing mathematics and the mathematics of dance[J]. Math Horizons, 2011, 18(3): 16-20.
[3] Forsythe W, Kaiser P. Dance geometry[J]. Performance Research, 1999, 4(2): 64-71.
[4] N. M. M. Ali, S. N. Udin, H. M. Adenan, S. K. S. Husain and N. A. Zakariah, The Existence of Geometry in Zapin Pat Lipat Dance. AIP Conference Proceeding, 2024.
[5] Iyengar Mukunda Kalpana, Bharatanatyam and Mathematics: Teaching Geometry Through Dance, Journal of Fine and Studio Art, vol. 5(2), pp. 6-17, 2015.
[6] Susan Gerofsky, Learning Mathematics Through Dance. Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture, 2013.
[7] Levie R. Curve fitting with least squares[J]. Critical Reviews in Analytical Chemistry, 2000, 30(1): 59-74.
[8] Hansen P C, Pereyra V, Scherer G. Least squares data fitting with applications[M]. JHU Press, 2013.
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