My Final PerformanceIA, Mathematics SLIntroduction:Bharatanatyam is a form of Indian classical dance that was originated about 2000 years ago in Tamil Nadu, (South) India. It is one of the nine officially recognized national dances of India. This dance is mainly known for its perfect postures, vivid expressions, and symmetrical positions. It requires immense balance and training in order to be perfect at it. This dance form has flourished internationally and has been adopted by numerous as it has proved to be beneficial fortune many who have been engaged in it. Some of the benefits include refining skills, improved blood circulation, increased self-confidence, better health and lots more. I started learning this dance at the age of 13, this year I will be completing my five years. Although I will be “graduating”, my journey will not be ending until I perform one last time. This final performance of mine, called Arangetram, will not only be a tribute to all my years of training but will also be examined one last time. This examination will be my final steps towards gaining a recognition of completion.Keeping in mind my upcoming performance, I thought why not try to combine math and dance together. This idea instantly struck me to pursue a research study in this particular dance form, as this subject is in my field of interest. Although along with researching and finding more out about this dance I wanted to do some calculations that I would be able to use for my upcoming performance, So, I decided that in the process of this research, I will be doing calculations that I personally will be using in the near future. The calculations will reach the different areas of the various components of the performance. These components include dance steps, postures, position, costume and the rubric. The exploration will give me the opportunity to get a deeper perception of the dance which will help me better my performance.By using some of the math concepts that are interlinked with this dance, I will be able to identify the key factors which when executed accurately will help bring out the best in me. Firstly, I will be discussing what the dance form is and later moving onto the necessary calculations.Bharatanatyam is a form of schooling, a study in fine arts. To begin with, the student is put into a beginner level, which can be compared to primary school where the child learns the basics and builds a strong foundation that will be used in the future.The student is usually at this stage for 1-3 years. The next stage is the intermediate level (middle school ), which lasts about 2-4 years, depending on the student’s potential to grasp the required abilities. The final phase is the advanced level which is like high school. This level, which approximately takes 2-4 years to complete, ends with a graduation which provides the student with credits that they can use in the future if they decide to apply for a degree to pursue a career in this field. .In order to graduate students need to prepare a final performance, Arangetram. This final performance marks the candidate’s graduation and therefore it is an extremely important part of this dance journey. The performance is marked by the respective teachers and the board of directors of the dance academy. This evaluation is done using a universal rubric (Figure 1) to judge the performer’s skill and whether or not he/she has justified their years worth of training. Figure 1:Arangetram, the final performance is a group project. Groups of three are required and a total of 80 minutes are given to showcase the performer’s talent. Although the actual showcasing of the dance Only the first 20 minutes is the prepared dance, rest of the time will be used by the examiners to clear any doubts and judge the performance. Apart from the singing and the expressions that are required, the major component of this performance is the actual dance. The dance can be broken down into three steps: position/stance, hand gestures, and feet movement. Upon mutual agreements, we decided that our trio should stick with just one position in which all of us could be viewed equally. We chose the upside down” V”- shape position where one will always stay at the back(middle) while the other two will be diagonal of him/her on different sides. Although there is only one position that we can perform in, the three of us can rotate between the three arrangements. To find out how many different ways we can interchange our positions, I decided to use the permutations formula. I chose it because permutation is an ordered combination and it is exactly what I needed to figure out how many different stances the three of us could take while still remaining in our standard ” V”- shape position. Then in the formula stands for the set size, and r stands for the number of spaces that can be filled. The “!” symbol, is known as the factorial, stands for the product of all positive integers less than or equal to n. Using the formula from the textbook I calculated the following:Formula: P (n,r) = (n!(n-r)!)?my equation ? P (3,3) = (3!(3-3)!)P (3,3) = (3×2×1(3-3)!)? P (3,3) = (6)? P (3,3) = 6Therefore, our trio can position ourselves in 6 different arrangements. I also used a calculator to confirm my answer (Figure 2:)Figure 2:An embroidered dress, elegant makeup, and lots of jewelry make up the final look of the dancer. Dress plays a key role because it gives the viewers a bright and colorful image. A traditional Bharatanatyam costume is a 4-piece dress (Figure 3) which consists of a blouse, pajama-style pants/ skirt, saree (drape), and a fan. The costume is custom made for each dancer varying upon the dancers’ size and flexibility. Figure 3: Figure 4:The fan is a vital component of the dance because many of the steps include the stretching and bending of legs, therefore when performing the fan will beautifully fan out and create a perfect arc which will leave a visually appealing effect on the viewers. This is the most basic posture and is known as Ardha mandalam. Ethically the fan should be fanned exactly 180 degrees but this does not happen in most cases. Although, dancers try to get as accurate as possible. The length of the material needed will depend upon the angle created, and the width is subject to the dancers’ height. The customization of the fan depends on the precision of the dancers’ ability to fan out their fan. Accordingly, the appropriate amount of material is used. To figure this out, each dancer is told to take the position (Figure 4) where the fanning will typically be at its maximum. To see how precise they are to 180 degrees and how much material they will need for the fan, the angle is measured. Subject to the angle created by the dancer, the length of the cloth needed to make the fan will vary. The length is determined by the dancers’ height from waist to the knees plus an extra 2-4 inches. For the following calculation I will be adding an extra 3 inches to each of the dancers’ height (waist to knees) Along with the angle, I will be using the arc length formula to determine the measurements I will be needing to provide my tailor with. There is nothing of sort such an as one perfect angle and one specific height as both of these factors depend upon the dancer. Therefore, to see the different ways a fan including myself. The different scenarios are as follows:* I will be using the arc length formula from the textbook. a= r?, where the r stands for the radius, in this case, the length, and the ? is the angle in radians. Another formula from the textbook that I will be using is the conversion of degrees to radians which is, radians= degrees×180?. The height in the following calculations means the measurement from the waist to the knees. The extra refers to the additional 3 inches each dancers fan will get. – All measurements have been converted from inches to cm. Scenario 1:R = 53 cm (height ) + 7.62 cm (extra ) = 60.62 cm?= 133 degrees = _____ radians. ? ( 133 degrees ×180?) ? 2.32 radsArc length = 60.62 cm × 2.32 rads = 140.6384 cm ?1.41 mScenario 2:R = 32 cm (height) + 7.62 cm (extra) = 39.62 cm?= 146 degrees = _____ radians. ? ( 146 degrees ×180?) ? 2.55 radsArc length = 39.62 cm × 2.55 rads = 101.031 cm ?1.01 m Scenario 3:R = 38 cm (height) + 7.62 cm (extra) = 45.62 cm?= 157 degrees = _____ radians. ? ( 157 degrees ×180?) ? 2.74 radsArc length = 45.62 cm × 2.74 rads = 124.9988 cm ?1.25 mAfter working out all the calculations by hand and rechecking them on a calculator. It has been concluded that the measurements (lengths) of the three distinct=nct fans will be ?1.01 m, 1.25 m, and 1.41 m. Moving onto the third and most important aspect of this dance. The expressions in this dance are not only shown through facial gestures but also the movement of hands and feet. The hand gestures are known as mudras, here are two types of hand mudras. Firstly the asamyukta hastas, which are single-handed mudras, there are 28 of them and recently 4 new have been added to the list. The double hand mudras are called the samyukta hastas, there are 24 of these. All the signs hold different meanings, for example, the double hand mudra- Katoaka-vardhana ( Figure 5) can be inferred as the denotation of marriage, coronation ceremony or worship. Bhramara, (Figure 6) a single-hand mudra which can be an action referring to a parrot, bee, wing, heron, and others.Figure 5: Figure 6:In total there are approximately 56 mudras/gestures that we can use, although that was just the hand gestures. Moving onto the feet is far more complicated than the hands. There are 10 postures (mandala), 9 feet postures (sthanaka), 6 regular feet postures, 10 stepping postures, 8 gaits (charis), 7 spiral movements (Bhramari ), and 5 jump movements (utplavanas). As a total that would be 55 various types of leg actions. As far as the dance goes for every hand movement there is a feet movement and it keeps changing as the song plays along. I want to know all the different variations I can add to my dance. For this, I will need to calculate how many different combinations of all the hand and feet actions are possible. I will be using the combinations formula from my textbook to figure this calculation because combinations are the selection of an object(s) from a set where the order does not matter. Like permutations, the n in the formula stands for the set size, and r stands for the number of spaces that can be filled. C (n,r) , repetition allowed = (n + r – 1)!r! (n-1)!Feet actions:C (55, 1)= (55 + 1 – 1)!1! (55-1)! ?551?55 possibilitiesHand Actions: C (56, 1)= (56 + 1 – 1)!1! (56-1)! ?561?56 possibilitiesWell now we have the separate possibilities but we need the combinations of both. To figure this out I need an equation that will give me the calculations of choosing one hand action and a feet action. This is why I multiplied the respective hand and feet actions equations.((55 + 1 – 1)!1! (55-1)!)×((56 + 1 – 1)!1! (56-1)!)? (55)×(56) = 3080Therefore, 3080 different combinations are possible.In conclusion, all the calculations that I have worked ou are related to my upcoming performance. This research study was not solely based on researching but it was also based on real-life situations. Such an exploration provided me with the opportunity of interconnecting two of my favorite fields of interest. I was able to make connections and calculate much of the required necessities for the dance. Bibliography: (URLs)Vipin, S. (2017, April 07). 5 Reasons why should Children Learn Bharatanatyam. 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