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Three intersecting cylinders


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#1 bonanova

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Posted 06 August 2012 - 06:54 AM

A classic problem solved by Archimedes before the invention of calculus, concerns two circular cylinders intersecting at right angles.
If each cylinder has a radius of 1 unit, what is the volume of space that is common to the cylinders?
For warm-up, you can figure out the answer - using calculus if you like.

Here's the puzzle of the day:
What is the volume of space that is common to three orthogonally intersecting cylinders of unit radius?

In both problems the axes of the cylinders intersect.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#2 Pickett

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Posted 06 August 2012 - 01:55 PM

Spoiler for Dust off the old math portion of my brain...

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#3 bonanova

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Posted 06 August 2012 - 07:36 PM

Spoiler for Dust off the old math portion of my brain...


Bravo, for accuracy and beautiful symbols. Two coveted stars!
bona_gold_star.gif bona_gold_star.gif
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 kbrdsk

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Posted 12 August 2012 - 03:10 PM

Is the three cylinder problem also doable without using calculus?
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#5 bonanova

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Posted 13 August 2012 - 07:26 AM

Is the three cylinder problem also doable without using calculus?


Well to be fair, Cavalieri's principle was the calculus dodge for the two cylinder calculation.
It's a near cousin to the integral calculus.
The three cylinder problem might succumb in a similar way.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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