The Naked Scientists

The Naked Scientists Forum

Author Topic: What form has the greatest surface area?  (Read 3869 times)

B.Kotzen

  • Guest
What form has the greatest surface area?
« on: 29/10/2009 18:30:03 »
B.Kotzen asked the Naked Scientists:
   
Dear Chris

Please would you kindly put your thoughts to the question which asks which form/facade has the greatest surface area, in nature and perhaps mathematically / architecturally?

Many thanks

Dr Benz Kotzen

School of Architecture
The University of Greenwich

What do you think?


 

Offline Mr. Scientist

  • Neilep Level Member
  • ******
  • Posts: 1451
  • Thanked: 2 times
  • http://www.facebook.com/#/profile.php?ref=profile&
    • View Profile
    • Time Theory
What form has the greatest surface area?
« Reply #1 on: 29/10/2009 18:48:12 »
Well, since the universe is said to have no boundary, then i would say any natural vacuum object with high volume structure, such as a supermassive black hole with a one-way surface we call a Horizon.
 

Offline RD

  • Neilep Level Member
  • ******
  • Posts: 8130
  • Thanked: 53 times
    • View Profile
What form has the greatest surface area?
« Reply #2 on: 29/10/2009 19:00:37 »
Repeatedly branching structures have high surface areas, e.g.
biological bronchial tree or the mathematical horned sphere.

For a facade perhaps some sort of corrugation based on fractal geometry ?
« Last Edit: 30/10/2009 09:32:36 by RD »
 

Online Bored chemist

  • Neilep Level Member
  • ******
  • Posts: 8666
  • Thanked: 42 times
    • View Profile
What form has the greatest surface area?
« Reply #3 on: 29/10/2009 20:17:18 »
 

Offline Don_1

  • Neilep Level Member
  • ******
  • Posts: 6890
  • Thanked: 7 times
  • A stupid comment for every occasion.
    • View Profile
    • Knight Light Haulage
What form has the greatest surface area?
« Reply #4 on: 30/10/2009 08:06:55 »
I see you are at the School of Architecture at The University of Greenwich, not far from me, so I shall pop my head out of the window and wave to you.

We had a thread here a short while ago on trees. Afraid I can't find it!

Anyway, I think that in nature, a contender for the greatest surface area would have to be 'Pando', a Quaking Aspen in Utah. It is a clonal tree which is estimated to be around 6,000 tonnes, covers 107 acres and has around 47,000 stems. Whoever counted the stems seriously needs to get a life! The individual stems live for around 180 years and the plant is estimated at 80,000 years old. It is considered the most massive living organism.

Taking into account its individual stems, the branches from those stems, the subdivisions of those branches, the leaves and, of course, the root system, I should think the surface area must be in the order of........

Sorry, my calculator just blew up, well it will certainly be more than a few square meters. Perhaps the nitwit who counted all those stems might like to work out the area.
 

Offline LeeE

  • Neilep Level Member
  • ******
  • Posts: 3382
    • View Profile
    • Spatial
What form has the greatest surface area?
« Reply #5 on: 30/10/2009 18:39:00 »
B.Kotzen asked the Naked Scientists:
   
Dear Chris

Please would you kindly put your thoughts to the question which asks which form/facade has the greatest surface area, in nature and perhaps mathematically / architecturally?

Many thanks

Dr Benz Kotzen

School of Architecture
The University of Greenwich

What do you think?

I'm afraid that you need to qualify/clarify this question a bit.

On the assumption that you're asking which simple 3D form has the greatest surface area per unit volume, then the answer is a sheet i.e. something where the depth is much smaller than its width and height.  Obviously, reducing the depth whilst maintaining the same volume will result in an increase in the width and height, and hence the surface area.  A good example of this is in gold beating - see the link below that shows how a 5 mm diameter 'nugget' can be beaten into a sheet with an area of 0.5 square metres.

http://en.wikipedia.org/wiki/File:Small_gold_nugget_5mm_dia_and_corresponding_foil_surface_of_half_sq_meter.jpg

However, we shouldn't forget about the area of the sides of a sheet, and while the area of the sides is negligable for a regular polygon or other relatively simple shapes, the perimeter of a fractal is potentially infinite, even when the area of the fractal is finite: when you plot the Mandlebrot set, the entire plot lies within a 2x2 square, and so must be finite, but the length of the perimeter is only limited by the resolution.  In theory then, it would seem that the area of the sides of a finite depth fractal could exceed the area of the fractal itself, even though it would still be a 'sheet'.
 

Offline Soul Surfer

  • Neilep Level Member
  • ******
  • Posts: 3345
  • keep banging the rocks together
    • View Profile
    • ian kimber's web workspace
What form has the greatest surface area?
« Reply #6 on: 01/11/2009 18:55:03 »
The sphere has the smallest surface area but there is no theoretical limit to the maximum surface area of a mathematically fractal surface however from a physical point of view the atomic structure of matter puts a limit to the maximum but this is very large indeed
 

The Naked Scientists Forum

What form has the greatest surface area?
« Reply #6 on: 01/11/2009 18:55:03 »

 

SMF 2.0.10 | SMF © 2015, Simple Machines
SMFAds for Free Forums