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Bearflag70
02-28-2010, 03:04 AM
This question popped into my head just before trying to sleep and is bugging the crap out of me.

If a square and circle have equal area, which has a larger circumference/perimeter?

runcible spoon
02-28-2010, 03:09 AM
The square. Actually, any shape, compared to a circle of the same area, will have a larger perimeter; circles have the lowest possible perimeter per area (or, as I tend to think of it, the most area per perimeter).

friedo
02-28-2010, 03:10 AM
This is pretty easy to figure out.

A square with an area of one has a perimeter of four.

Since the area of a circle is pi*r2, a circle with an area of one has a radius of sqrt( 1 / pi ), which is roughly 0.56, and thus a circumference of 3.52.

chromaticity
02-28-2010, 03:13 AM
If I remember my Physics lessons correctly, this is the reason why liquids form spherical drops and circular splatters, because of surface tension, they reduce their surface area,

Bearflag70
02-28-2010, 03:13 AM
THANK YOU!

Off to bed.

Any other interesting bits of info I will enjoy in the morning.

code_grey
02-28-2010, 03:14 AM
the square will have larger perimeter, for generic discussion see here http://en.wikipedia.org/wiki/Isoperimetry

This is reflected in the story of queen Dido/Elissa the founder of Carthage. Allegedly, she showed up in Tunis with a small band and convinced the local ruler to sell her as much land as can be covered by an ox hide. She then cut it up into a thin line and used it to encircle the most area for the same perimeter - namely a circle around a hill. Not a square or any other figure.

retsin2000
02-28-2010, 03:20 AM
This is the corner of Hoedown Dr and Square Circle near Columbia MO. Probably won't help you with you question although it seems to be answered already. I lived a couple doors down from here many years ago. Your question reminded me of Square Circle. Hoedown isn't a bad street name either.
This url generated by the Weird Url generator, it just sounds dangerous.

NinetyWt
02-28-2010, 10:03 AM
A fun book to read about Pi and the squaring of the circle is A History of Pi, Petr Beckmann.

Johnny L.A.
02-28-2010, 10:18 AM
∏r2. So my cornbread r round.

:p

'Cause I make my cornbread in a cast-iron skillet.

Chronos
02-28-2010, 12:24 PM
This is reflected in the story of queen Dido/Elissa the founder of Carthage. Allegedly, she showed up in Tunis with a small band and convinced the local ruler to sell her as much land as can be covered by an ox hide. She then cut it up into a thin line and used it to encircle the most area for the same perimeter - namely a circle around a hill. Not a square or any other figure.A semicircle, actually, right up against the coast.

We were just discussing this in another GQ thread (http://boards.straightdope.com/sdmb/showthread.php?t=553892), still active.

septimus
02-28-2010, 12:59 PM
(Regarding Dido's Problem) A semicircle, actually, right up against the coast.

Yes. I think wikipedia is to blame for the confusion, not your quotee. Apparently some zealous Wiki editor decided to merge the "Dido's Problem" page into the "Isoperimetric Inequality" page and (although Dido's Problem is stated correctly if briefly there) somehow the problem ended up misstated on the page for Dido herself!

What's the technical term for a work of writing so well polished that any futher attempt at improvement is likely to worsen it instead? Whatever that is, many Wikipedia pages seem to have reached it. :mad: There's a lot of good info at Wikipedia you have to click History to find. :smack: