Assignment 3 Reflection

Oops! Guess I was too excited about dancing to pay attention to the graph

 Through this project, I learned a lot about Aryabhata's sine table, some of his sine/geometric relationships, and more about Indian dancing. One of the points I messed up on (and I will add a note to the slides) was that I actually misrepresented the dance. If I was to go back and do it again, I would have done a total "Kathak fusion" (not just the hands) where it just went right, left, right, left, etc. for footwork but I instead performed the proper footwork which was right, left, right, left heel, left, right, left, right heel, right etc. Susan, when you asked us about this during the presentation, I thought you were talking about the heel step, in which case, I would have students potentially come up with a way to represent that (e.g. hole in the graph or some other indicator). Additionally, students might pick up on the fact that I stay at centre position for much longer during the first portion, but it gradually becomes more like a sine graph as you get faster (because you have to pick up your feet faster to get more steps per beat). When that happens, the amplitude should get shorter as well (you can't lift your knee as high when you have to do 4 taps in one beat!) and so on, so there are a lot of exercises that come out of this that deal with different features of sine - but I should have mentioned these in the slides. 

One of my favourite discoveries through this project was that Aryabhata referred to Rsine as half-chords and that sine is actually a translation mistake as half-chord made its way from India to the Arab world, and finally to Europe in Latin as "sinus." Ptolemy had also done a half-chord table, but the Indian version was unrelated to it. Also, Aryabhata chose R = 3438' as his radius so that the circumference of the radius would be as close to 21600 = 360 x 60, so one unit along the arc of the circle would correspond to one minute (Berlinghoff & Gouvêa (2015). Math through the ages). I still wasn't able to figure out or make the connection between why this would be helpful exactly (i.e. why measure length in degrees/minutes as opposed to a standard measurement), but it would be an interesting topic to explore. I would have loved to express these ideas during our presentation as well but it was difficult to fit everything we wanted into the allotted time. However, I still think the history and dance applications would be a great introduction to sinusoidal curves in a math classroom (and allow us to explore dances we enjoy already through a mathematical lens).