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  • Exams
    May 2019
  • Country
    United States
  1. I'm starting to work on the topic you suggested: optimizing all three types of torii (ring, horn, and spindle) as well as ellipses, hyperbolas, and parabolas. Do you have any resources for getting started with spherical/cylindrical coordinates like you suggested? I can't grasp the concept well enough to actually use it in my IA yet.
  2. @kw0573 I know you already suggested me not to do it, but what if for the GDP vs HDI, I don't derive the polynomial regression, just use the least squares method, and then use some kind of distance correlation to relate the two equations. Why is it a problem if it's too stats based?
  3. You are really really helpful! Thanks so much. Would you mind if I asked you a few more questions tomorrow? Thank again.
  4. @kw0573 Would you use something like this: https://www.youtube.com/watch?v=tMVwXglUp60? It's a proof for the surface area of a ring torus.
  5. @kw0573 How would I go about approaching this without Pappus? Would it be something like this: http://whistleralley.com/torus/torus.htm? Based on your advice, I'm planning to not reference Pappus, but derive the volume of the torii by myself? This leads me to another question, however: how can the surface area of a torus be found without Pappus?
  6. @kw0573 Thank you, this is so helpful! My teacher told me that when I use Pappus' Centroid Theorem (which gives the volume/surface area of ring/horn torii), most of the work is already done for me, so my actual optimization is pretty straightforward from there. How can I avoid this criticism for the rest of my original IA? By non-cartesian, do you mean polar or complex? (If so, I'm not really sure how to incorporate this into the IA..) The other conic sections you're referring to are parabolas, ellipses, and hyperbolas, correct? Would just optimizing all of these solids of revolution for maximum surface area be enough to make a decent IA? Thanks again!
  7. @kw0573 No, our class is going to study Topic 9 in a few weeks, but we haven't started yet. That's what I was worried about whether I could teach myself Solow-Swan. You mentioned HDI vs GDP was somewhat lacking; do you have any ways I could increase its difficulty level?
  8. @kw0573 Do you really think so? I'm not so sure, because we haven't learned differential equations in our class yet. If I were to do Solow-Swan, aren't the limitations and assumptions already well known?
  9. Another idea just occurred to me. What if I used the least squares method to predict how HDI (human development index) will change in the future by plotting a polynomial regression for it? Since HDI is often criticized for being too tied to the GDP of a country, would it be a good idea to find a polynomial regression for the GDP per capita and compare both of them? Is this idea complex enough for Math HL? Also, if I did this, in what ways could I compare GDP and HDI? Should I do something like a statistics correlation test (like the chi-squared test or distance correlation test) to add on to it?
  10. My original IA topic for HL Math was optimizing the surface area of a ring, horn, and spindle torus given a fixed volume. My teacher told me that it was too simplistic, and that there was not enough original math in the paper, so I'm searching for a new topic. I came across the least squares regression, which is used for polynomial regressions and involves calculus. I was thinking about maybe applying this to some aspect of economics/markets/businesses. I found the Solow–Swan model as a potential starting point. Would it be a good to use something like this for my IA, and would it be complex enough for a HL Math IA? If not, how could I make it more original and more complex? I'm also not sure what kind of variations I could put on this equation to customize to my IA specifically. The Solow-Swan model involves nonlinear ordinary differential equations (Topic 9), which is something that we haven't learned yet but will in a month or two. Because of this, would you recommend that I try to teach myself this concept for my IA? I'm just really confused at this point because my teacher isn't offering any more guidance.
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