Anything else we may be able to answer for you today? ***************************************************** 01-07-05, 09:41 PM aminator2002 Interesting... it seems like all the calculations are based on finding the surface area of a spherical object and then deducting out the oceans. I can't find any that include topographic changes... a mountain has more land area than a large open plain. Right?
Or maybe that is part of the calculation and I'm not seeing it.
01-08-05, 01:14 AM Professor Be careful: the area might turn out to be infinite, if you keep zooming in at ever higher magnification to examine surface contours at ever smaller scales.
"How Long Is The Coast of Britain?" was one of the chapters in Benoit Mandelbrot's seminal work on the mathematical theory of fractals. Modeling lenths of bays containing coves containing inlets, etc. in endless nested regression will lead to non-convergent series. One may conclude that coastlines can have infinite length.
The classic Koch Snowflake Curve, constructed as triangles upon triangles ad infinitum, can be shown using high school algebra to have a finite area enclosed by an infinite perimeter.
By analogy, the surface area of a fractal solid could have a finite volume enclosed by an infinite surface area.
You can get a sense of this from the fact that a gram of activated charcoal has an absorptive area on the order of a tennis court. Ditto for the lungs in your chest.
The earth is said to be smooth as a cueball; the Himalayas barely register as a fine scratch. So projecting the continents onto a perfectly smooth spheroid (images from space will do nicely) makes a pretty good approximation if you don't look at detail too finely. You can limit the level of detail by imposing a minimum radius of curvature of contours. Something like one kilometer for practical purposes.
To the extent that rock, soil, vegetation, etc. have fractal geometry, the total surface area approaches infinity.
But true fractal geometry is an abstract mathematical construct. As you zoomed in on the real world you would get down to the scale of the molecules of bulk matter, endowed with great uniformity and yet quantum fuzziness. I'm not sure it's meaningful to measure "surface area" below that scale.
Still, a measurement of surface area using, say, one-micrometer detail might yield an area many orders of magnitude greater than the satellite-image minimum.
01-08-05, 12:39 PM mattlynda so THATS why no one in my old science class got that answer correct. teach me to go through old school work. Wink
01-08-05, 10:42 PM Professor If science class was before the 1980's then you & your teacher are off the hook on fractals Smile I'd stick to Jusork's answer!
01-09-05, 10:54 AM mattlynda I'M barely before 1980. Wink to be fair, it was jr. high science. he liked to do stuff like that to us.
01-16-06, 08:43 AM Roger Ramjet Using jusork's original first-order approximation of 57,500,000 sq. miles the answer is actually 1.603x10^15 sq. feet; his answer is only off by a factor of a million!
01-16-06, 12:38 PM jusork Oh! Thanks a bunch, Roger. I had a feeling my math was off because I'm the worst at math. A big welcome to Answerpool.
02-10-06, 05:31 PM mozart56 World's Atlas gives another answer to it.
Land Area (148,647,000 sq km)which translates into 92,364,935, square miles.Then in square feet :2,574,986,603,904,000
02-10-06, 06:51 PM methos Mozart - you're conversion is wrong (specifically, the first conversion from square km ti square miles, where you used the factor between linear kilometers and linear miles). 148,647,000 km2 is 1.6 × 1015 ft2, the same value given by Roger Ramjet based on Jusork's square mile value.
02-11-06, 12:05 AM mozart56 OK, I'll keep my nose in the trivia section,I'am better overthere!
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