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"If all three dimensions of a human being scaled equally as they grew, then a formula of the form weight/height3 would be appropriate. They don't! However, weight/height2 is not realistic either.
A better approximation to a complex reality, which is the reform I wish could be adopted, would be weight/height2.5. Certainly if you plot typical weights of people against their heights, the result comes out closer to height2.5 than height2."
"If man increased equally in all dimensions, his weight at different ages would be as the cube of his height. Now, this is not what we really observe. The increase of weight is slower, except during the first year after birth; then the proportion we have just pointed out is pretty regularly observed.
But after this period, and until near the age of puberty, weight increases nearly as the square of the height. The development of weight again becomes very rapid at puberty, and almost stops after the twenty-fifth year. In general, we do not err much when we assume that during development the squares of the weight at different ages are as the fifth powers of the height; which naturally leads to this conclusion, in supporting the specific gravity constant, that the transverse growth of man is less than the vertical.
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"Does my BMI look big in this?" Pete Wilton, University of Oxford
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