S_Orbital Posted June 9, 2019 Report Share Posted June 9, 2019 Hello everyone, I was looking for math IA ideas and I thought of trying to prove that the double angle formulae are correct. This fits in with the SL syllabus because I use the formulas and the Unit circle. Do you think that this sort of exploration would be appropriate to get around a level 6-7? Does it have potential? Thank you in advance Reply Link to post Share on other sites More sharing options...
kw0573 Posted June 10, 2019 Report Share Posted June 10, 2019 The topic in its current form is very much insufficient for a SL Math IA. You should look for math topics that go beyond a simple formula. Reply Link to post Share on other sites More sharing options...
S_Orbital Posted June 10, 2019 Author Report Share Posted June 10, 2019 3 minutes ago, kw0573 said: The topic in its current form is very much insufficient for a SL Math IA. You should look for math topics that go beyond a simple formula. Thank you for the reply. I've got a new idea now. How do you think I could model vibrations of an object such as a rubber band mathematically? Do you also think it would be appropriate to look at resonance waves? Thanks again Reply Link to post Share on other sites More sharing options...
kw0573 Posted June 10, 2019 Report Share Posted June 10, 2019 Do you mean standing waves or resonance? I suggest not to venture into physics if you are not strong in physics. (The math of resonance is beyond Math HL). I don't usually like to recommend modelling because i) it is hard to verify your results ii) the math is usually not very complex iii) a lot of number crunching that is prone to errors iv) it is difficult to communicate the ideas systematically. A different route is to explore relationships between topics, usually through solving a problem. For this route it is usually easier to verify the result either because you can plug into an online calculator or find other people solving similar problems. For this route I recommend looking through videos by 3Blue1Brown and Mathologer for inspirations. For modelling, I strongly recommend exploring/deriving the formulae for linear regression before using it. It is usually better to "calculate" parameters rather than through trial and error. One approach is to linearize the equation to be fitted, apply linear regression (such that the slope and y-intercept are expressions of the original parameters), then solve for the parameters. You can see how complex modelling gets if you do it rigorously. Ideally, it should be a mathematically elegant topic that you understand well and can explain clearly. Reply Link to post Share on other sites More sharing options...
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