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March 29, 2024, 07:54:07 pm

Author Topic: Area question  (Read 2621 times)  Share 

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Albertenouttaten

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Area question
« on: August 22, 2021, 02:43:47 pm »
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Hi all,
Getting a bit stumped on how to approach this question. I'm having trouble with part b. I've added part a for context.

I've tried doing 600/78.54 which would be theoretical minimum required sprinklers however that would be assuming no overlap. Unfortunately my brain isn't wolframalpha and I'm having trouble thinking about the orientation of the sprinklers for there to be 8 with 0 overlap? Or am I just approaching this question all wrong?

schoolstudent115

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Re: Area question
« Reply #1 on: August 22, 2021, 04:43:34 pm »
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Hi all,
Getting a bit stumped on how to approach this question. I'm having trouble with part b. I've added part a for context.

I've tried doing 600/78.54 which would be theoretical minimum required sprinklers however that would be assuming no overlap. Unfortunately my brain isn't wolframalpha and I'm having trouble thinking about the orientation of the sprinklers for there to be 8 with 0 overlap? Or am I just approaching this question all wrong?
Well I haven't solved this yet, but I'm 99.999% sure it is impossible to fit them with no overlap, given that the best case is you get 2 points of tangency between a circle and any other two circles, and as concavities will be flipped, you can't possibly fill all the area without overlap.
My solution would be to fit all the 2x2 boxes with full circles without overlap, then on the edges add semicircles, and in the dead zones inside add some full circles, and in the corners add quarter-circles.
« Last Edit: August 22, 2021, 04:46:31 pm by schoolstudent115 »
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2022-2024: University of Melbourne, BSci (Major in Mathematics and Statistics)