Math Is Fun Forum

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Area over volume.

I was walking around a second-hand furniture store
called Penelope's, and I noted that if they partitioned
the rooms up more, they would have more wall space
for pictures they are selling.  But then they would run
into problems to do with volume, such as furniture not
fitting into tiny rooms.   I thought at first, wow! There's
no limit on surface area, when you divided up a volume.
But there are practical disadvantages.
(This topic is quite silly, so delete if want to after a week.)

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igloo myrtilles fourmis

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Area over volume.

hehe! Well a circular room would provide the least amount of wall space possible. If they wanted to maximize the amount of wall space, they could make the room shaped like a star, or better yet, kosh snowflake. That has an infinite amount of surface area! :-P

below is a kosh snowflake with a recursive depth of 2. Wrote a recursive function to draw this as an excersize in recursion.

Last edited by mikau (2007-06-04 05:52:40)

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A logarithm is just a misspelled algorithm.

LQ

Real Member

Registered: 2006-12-04

Posts: 1,285

Re: Area over volume.

That would be really awesome, perhaps that was what they wanted to do when they built stonehenge, hehe, I don't believe so, hehe. NOT. Ofcourse not. It would be like saying "stonehenge was a fungus". hehe.

I apologize.

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I see clearly now, the universe have the black dots, Thus I am on my way of inventing this remedy...

mikau

Member

Registered: 2005-08-22

Posts: 1,504

Re: Area over volume.

well for the record, John E. Franklin, i just did a quick maximization computation and it turns out that if we are dealing with a rectangular display room, a square provides the LEAST amount of wall space possible, but you can get as much wall space as you want by making the room narrower and narrower (assuming the floor space remains at a constant). If you make the room infinitly narrow, you have an infinite amount of wall space! :-)

but if you actually wanted to maximize the amount of wall space for a given floor size, and still use a rectangular room, the trick would be to make the room as narrow as practicality allows.

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A logarithm is just a misspelled algorithm.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Area over volume.

Your kosh snowflake reminds me of this shape with 100 sides I
drew 13 months ago.  http://www.mathsisfun.com/forum/viewtop … 370#p34370

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igloo myrtilles fourmis