Maths IA help - dance, draw, sew, game theory

[Vsu]

Hi,

I have a couple of very rough ideas (or really, just topics) for my Maths IA, but I don't know if any of them will work. Also, if you have any suggestions in the areas listed below, for how to turn them into a good maths IA (regardless of what I've written beside the bolded word) that'd would be MUCH appreciated.

1. Dance: I was thinking maybe investigating whether an infinite pirouette is possible, like the angle the bent leg needs to be at, the angle the other leg pushes off of, arm position and force/power of pushing off? Or looking into the maths of a leap (grand jete), maybe area under the curve?
    
2. Drawing: I really enjoy drawing, and I was hoping to somehow find maths in it? I was thinking maybe I could make a drawing using functions e.g. https://www.desmos.com/calculator/xatpypbly6 but I don't think that really investigates anything. I found something about how Van Gogh's Starry Night's paint strokes actually reflect Kogmorov's (sorry for butchering his name) Equation that is the most accurate equation for modelling Turbulence or something like that? But I think that's far too complicated for an SL maths IA. 
    
3. Sewing: sewing is a hobby of mine, and I thought it was probably an area that would have a lot of maths in it, but most of my research could only find elementary maths, like sizing or geometry. Do you know if there's any maths I can use to look into changing 2D pattern pieces to fit a 3D figure, or something like that? Or just anything to do with sewing, really.
    
4. Game theory, prisoner's dilemma: I read about how prisoner's dilemma shows human behaviour of how we cooperate with one another, and do so consistently, but then after a while, one party will break the trust, causing them to fall into a period of uncooperation. But then the cycle repeats, and I was thinking maybe this sounds like a sine curve and I could use it to model war and maybe predict when the next big war might be? On a side note, I was thinking of using a computer program that essentially "plays" prisoner dilemma with you, and use the data from that to sketch a graph or something. The problem is, I think one my classmates has also chosen to do the prisoner's dilemma. 

 

Or if none of them work, any other ideas would be so helpful too. If that's the case, I think I'm interested in calculus and functions, graphs. Other random topic ideas I've had are: origami, exercise, the fourth dimension (though I think this might be too hard), hexaflexagons, rainbows.

Please, any suggestions or feedback would be so good, I'm really worried about this. 

[kw0573]

Dance: Infinite pirouette only possible if no friction, but if no friction the dancer cannot even spin in the first place.

Customizing a function is ok idea. It could work if you bring up some conic sections, parametric equations, trig/periodic functions, and/or exponents.

I didn't take Econ but I think Game Theory, a lot of the times, assumes selfish/ulterior motives, and often that collective decision-making is impossible. I think unless you know a lot about game theory, an IA will likely end up superficial. 

I strongly recommend this YouTube channel: 3Blue1Brown https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw. It has a lot of videos of advanced topics made accessible to high school students and illustrates many many connections not discussed in textbooks

 

[Vsu]

1 hour ago, kw0573 said:

Dance: Infinite pirouette only possible if no friction, but if no friction the dancer cannot even spin in the first place.

Customizing a function is ok idea. It could work if you bring up some conic sections, parametric equations, trig/periodic functions, and/or exponents.

I didn't take Econ but I think Game Theory, a lot of the times, assumes selfish/ulterior motives, and often that collective decision-making is impossible. I think unless you know a lot about game theory, an IA will likely end up superficial. 

I strongly recommend this YouTube channel: 3Blue1Brown https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw. It has a lot of videos of advanced topics made accessible to high school students and illustrates many many connections not discussed in textbooks

 

Dance: do you think that I can just look at the maths of a pirouette and leap then, rather than finding if infinite pirouettes are possible. 

Draw: I asked my teacher if it was possible, but she said there was no point to it. Even if I did include all those different functions, isn't it just a list of functions that form a picture? Do you have any suggestions for how I could spin that into an actual investigation/exploration? 

Game Theory: ah ok, thank you. I'll cross that off the list then.

I was doing some more research before, and I was looking at rainbows. There seems to be a lot of maths in the angles, reflection, refraction and Snell's law etc. but I'm not sure what the exploration part would be, and if it's too much physics? 

And thank you! I'll check out that youtube account. 

[kw0573]

For pirouette/leap, if you can include a lot of math from SL or above, it's an ok topic.

From the perspective having most mathematics, create your own curve/graph is most flexible. Generally people go for route of recreating a picture. Out of the topics you suggested this is the best one and least likely to get stuck. 

Optics / light phenomena is good if you know what to include. Otherwise I don't think Snell's Law is advanced enough.