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Exploration on Gabriel's Horn

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Hi everyone,

This is probably my second topic on IB Exploration HL, but I have finally chosen a topic which I find interesting and fun to investigate. I am investigation the Gabriel's Horn Paradox and the limitations to it (why it isn't technically that much of a paradox).

I wanted to ask you guys if you know about this paradox? If you do, what limitations do you see to this paradox? I have read about it being a special case, like harmonic series. Can't really understand that! If anyone could help out... http://en.wikipedia.org/wiki/Gabriel%27s_Horn#Apparent_paradox

Furthermore, what should I include in the exploration? Should I start by actually showing proof of the paradox and then getting into limitations?

Opinions on how to structure an exploration are welcome!

Thank you guys!

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Well, I read the wikipedia page and the first thing that comes to mind is to actually find its volume by using core content from the HL course - using integrals and rotating curves to find volumes of shapes, and improper integrals. Then you can try to find its surface area by differentiating the equation you have for your integral. Afterwards, discuss the implications of the "paradox" and explain why it isn't exactly a paradox. You could also mention other shapes that do this, like the Koch Snowflake. I don't what else you could do, and whether or not that would suffice for an IA. Either way, good luck!

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