The document discusses a project that explores the intersection of mathematics and traditional Odissi dance, highlighting the potential for interdisciplinary study of dance as a knowledge system. It details the mathematical mapping of dance postures, such as 'Abhang' and 'Tribhang', using geometric shapes like squares and circles, and aims to enhance teaching methods for dance. The study emphasizes the importance of analyzing dance through multiple lenses, moving beyond its cultural and mythological context.

2. ACKNOWLEDGEMENT
• I would like to express my heart felt gratitude to my
maths subject teacher Renu Chandra ma’am who has
helped me doing this fun and wonderful project about
maths logic of Odisha.
• I came to know much more about the real world and
the importance of the subject. She opened my eyes to
see the world in a very different point of view and
analyse the life surrounding us. I give her the deserved
love and gratitude she deserves.

3. Studying traditional dance forms using an interdisciplinary approach expands
what it means to study dance and also helps understanding dance forms with
greater clarity.
 It highlights the fact that being a traditional dancer is more than just being a
performer; dance embodiment becomes a space of learning through an
amalgamation of humanities and sciences.
This project is built around the mathematical study of Odissi dance.
Since there is almost no study in this field this project first confirms the
possibility of study in this field then provides a base for further research.
ABSTRACT

4. INTRODUCTION
• This is a study that examines different postures of Odissi Dance using a
mathematical approach. Using the data acquired, the project aims at expanding
traditional methods of teaching dance technique and creating a method of
understanding the Odissi form mathematically. Using a mathematical approach to
teach adds to the traditional imitative mode of learning. Exploring traditional
dance forms through other disciplinary approaches creates a platform to engage
in critical questioning and examination of the dance form. This can be done
through learning the dance form or by studying its various aspects; that is,
allowing usage of multiple lenses to look at the dance forms. Dance becomes
more than just a sacred system; it now can be viewed as a knowledge system.
This means rather than viewing traditional dance as mythological or religious
sentiment; dance can be viewed as an object of interdisciplinary study.

5. METHODOLOGY
• The body while in dance posture broadly speaking forms many geometrical
shapes but all postures can be mapped within squares and circles. “The
centre of the wheel (chakra) of the Vedic and Upanisadic image corresponds
to the navel of the human body.
• Thus we have a pictorial image of Man set in a frame-work of a circle with
the navel at its centre and a vertical median corresponding to one diameter
of the circle.
• Kapila Vatsyayan further goes on to explain each movement and its deviation
from the vertical median.
• The consequence of exploring the furthest symmetrical extensions from the
vertical median is formation of a square within the circle. All postures can
thus be mapped using the square and circle and base lines.

6. • The body while in dance posture broadly
speaking forms many geometrical shapes but
all postures can be mapped within squares and
circles. “The centre of the wheel (charka) of the
Vedic and Upanisadic image corresponds to the
navel of the human body. Thus we have a
pictorial image of Man set in a frame-work of a
circle with the navel at its centre and a vertical
median corresponding to one diameter of the
circle.” Kapila Vatsyayan further goes on to
explain each movement and its deviation from
the vertical median. The consequence of
exploring the furthest symmetrical extensions
from the vertical median is formation of a

7. ABHANG
• Odissi posture in which, all the weight of the body is shifted
to one leg. Figure shows the similarities in sculpture and
dance posture of the posture Abhang shows how the posture
Abhang can be visualised using lines.

8. BLUE ANGLE (AT THE
WAIST): 157.5 DEGREES
RED ANGLE (BETWEEN
THE LEGS): 22.5
DEGREES
YELLOW ANGLE (AT THE
KNEE): 67.5 DEGREES
Similar to Tribhang the green
angle here represents the
deviation of the waist from the
central line. Comparing
the deviation one can see how
Tribhang and Abhang manifest
differently in the upper body.

9. CHAUKA
• “Chauka literally means square, which represents the first completely
stable structure.Chuaka is a basic odissi stance where the weight of
the body is distributed equally on both the sides. In Chauka the heels
face the centre; the toe point outwards and there is a distance of
about one foot between the two heels. The knees are outturned and
the thighs are bent.”
• There is no deviation from the central axis in the upper half of the
body. The symmetry of the body around the central axis in the lower
half of the body (below the Kati sutra marked blue in Fig (1) is what
differentiates Chauka from other postures. This is now mathematically
confirmed and can be visually appreciated.

10. 1.The black lines on
the image show the
original
2.Chauka by Guru
Kelucharan
Mohapatra

11. •Green Angle: 90
degrees
•Orange Angle:
135 degrees
•Blue Angle: 67.5
degrees

12. TRIBHANG
• “The word tri-bhanga means three breaks. The
tribhanga is evolved by one half of lower body
remaining static along the central plumb line
while the other leg usually crosses the first. Half
of the body from the torso upwards deflects in
the opposite direction. The head or neck provides
the third deflection. The tribhanga is achieved by
a sharp deflection of the hip from the horizontal
Kati sutra, and the head deflecting to the same
side as the hip. The bends are made at the knees,
the torso and the neck.”

13. The mathematical study makes it clear that this is A complex posture and
proper and accurate analysis of this needs better technology. A very
interesting observation is that though the second bend in the body is at
the waist .Its deviation from the central vertical line is to be measured at
the joint of the chest and neck (angle marked green in the image).
(Unfortunately the measurement of this angle was beyond the scope of
the project). Another observation is that on extending the lines drawn to
represent the calves downward into the ground A 90 degree angle must
be obtained. (This observation came from studying the human form while
in posture)
Yellow Angle (head
deflection): 33.75
degrees
Blue Angle
(between the legs):
90 degrees