Ratio of Volume to Surface Area in Humans
Date: 12/09/1999 at 20:01:05 From: Frances Hall Subject: Volume and surface area Hi: My students are studying giants and we are trying to determine the proper or healthy ratio of volume to surface area for humans. Can you help?
Date: 12/10/1999 at 09:19:50 From: Doctor Peterson Subject: Re: Volume and surface area Hi, Frances. I don't know that there is a specific ideal ratio; and you'd probably want to ask doctors or medical researchers rather than mathematicians if there is. What I can tell you mathematically is that this ratio varies depending on both shape and size, being proportional to height if the shape is the same. A larger person of the same shape would have a greater ratio, which could cause overheating problems, so that it might be preferable to have a thinner shape to decrease the volume and improve cooling; but on the other hand the larger volume- to-cross-sectional area ratio would cause excess stress on bones, making it preferable to have a thicker shape to increase the bone strength. In other words, I don't know that volume to area alone would give a good indication of health. But let me know if you find otherwise; it may be that within the normal size range this ratio does matter. If you can find the book _Men, Ants, and Elephants: Size in the Animal World_ by Peter Weyl (1959), I would recommend it. It deals with exactly these issues in an entertaining way, explaining why elephants have thick legs, need big ears to help cool their bodies, etc., while ants have proportionally thinner legs, and don't even need lungs. It is a fascinating subject to study, and involves a nice combination of math and science. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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