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Would finding the surface area of a hyperbolic paraboloid surface be a good enough topic for Math HL IA? I figured that I could use a pringle chip as my main reference for measurements and I could evaluate on the different ways I can approach the calculation (i.e. instead of using hypothetical measurements to find out the a and b variables of the hyperbolic equations I could graph out the x,y, and z plane individually and find out the variables from there).

 

This involves multivariable calculus which is a topic that is outside of the syllabus, but I'm afraid that it will be too short of an exploration as all I'm doing is calculating the surface area of the shape. If anyone wants to chime in and give any advice that would be greatly appreciated.

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I'd say try to gauge your teacher's response. If he/she is enthusiastic, that's a good sign. If he/she is unenthusiastic, then that is a good sign to not do it. I'm in Calc III right now and we just started surface area of these shapes yet. If I remember correctly, my teacher shot down a similar proposal from my friend, but it's the IA so your teacher might love it. It seems to be me like it might be too brief. It's really just one/two integration problems. I mean you could do volume (a very similar double integration problem) of a 50 Pringles stacked (or however many are in a box). I'd really be cautious. I don't think there's much enough to do here unless you expand your vision or change topics. But best practice is to talk with your teacher.

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As for all topics, if you can make connections from calculus to other math topics, such as trigonometry, sequence/series, complex numbers, vectors, or probability then it's a good topic. I think the topic as presented, can score 14 ish but if you are aiming for anything higher you should further develop this or choose something else. 

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4 hours ago, Nomenclature said:

I'd say try to gauge your teacher's response. If he/she is enthusiastic, that's a good sign. If he/she is unenthusiastic, then that is a good sign to not do it. I'm in Calc III right now and we just started surface area of these shapes yet. If I remember correctly, my teacher shot down a similar proposal from my friend, but it's the IA so your teacher might love it. It seems to be me like it might be too brief. It's really just one/two integration problems. I mean you could do volume (a very similar double integration problem) of a 50 Pringles stacked (or however many are in a box). I'd really be cautious. I don't think there's much enough to do here unless you expand your vision or change topics. But best practice is to talk with your teacher.

 

My teacher didn't discourage me from doing the topic when I proposed it, but then again, I don't know how much I can trust their judgment because my IA will be moderated later on

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30 minutes ago, kw0573 said:

As for all topics, if you can make connections from calculus to other math topics, such as trigonometry, sequence/series, complex numbers, vectors, or probability then it's a good topic. I think the topic as presented, can score 14 ish but if you are aiming for anything higher you should further develop this or choose something else. 

My goal is to get 16 at the very least. I don't think I can change my topic at this point as my draft is due in about a week, and I'm struggling to find ways on how I can expand this topic to create a more in-depth exploration :(

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44 minutes ago, kdbruh2 said:

My goal is to get 16 at the very least. I don't think I can change my topic at this point as my draft is due in about a week, and I'm struggling to find ways on how I can expand this topic to create a more in-depth exploration :(

I cannot give you specifics but try compare to eliptic paraboloid and try work in complex numbers because the general form just differ by a negative sign.

 

Edited by kw0573
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