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In math, there are special numbers, like Pi (3.14159...) and e (2.71828...). In chemistry, there's numbers like avogadro's number (6.0221413e+23). For example a circle can be defined in terms of 2 * Pi.

Are there any significant constant numbers in biology that define the shape of an organism (ex: mammal)? I'm talking about stuff like shoulder to hip ratio or length of an organism, etc?

Here's an example that came to mind - different fetuses developing into different organisms. Is there any constant that is the same for these at some stage of development? Like the ratio of head to tail?

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A fundamental idea of biology is individual variation. Though I don't know, I expect that there would be few, if any, constants shared between members of a group (outside of the molecular level). –  canadianer May 1 at 23:32
    
The golden ratio turns up in a lot of places, if that's what you mean –  swbarnes2 May 2 at 4:46
    
To give context to the question: I'm interested if there are some numerical patterns to gene expression during organism's development. –  Alex Stone May 12 at 16:34

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I don't know if this is what you mean, but take a look at BioNumbers.

Also, mathematical constants like pi are different from physical constants. Mathematical constants are true in a mathematical (logic) sense, and do not need to be related to any physical quantity. They are derived by logic. Physical constants, on the other hand, typically describe an observed relation between two types of quantities. They are derived by measurement.

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I think you have the direction of causality reversed. Due to either physical, chemical or dynamical properties of cells and organisms, it would certainly be possible to see patterns of constants emerge when making some measurements. I don't think you can say that the mathematical constants define any aspect of an organism. The Golden Ratio, or phi, was brought up as a recurring pattern in nature (e.g., the spiral pattern of snail. shells and sunflower seeds) but these are emergent properties of a physical system bound by physical constraints, and it so happens some pattern is used because it is efficient (in whatever sense that may mean).

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There are lots of examples of human body parts demonstrating the golden ratio. –  biogirl May 2 at 16:05
    
Any scientific references on the appearance of the golden ratio in nature? From what I know this is highly debated. –  Bitwise May 3 at 18:09
    
There are 20 references concerning facial symmetry and the golden ratio indexed on PubMed, and nearly 800 mentioning the golden ratio itself. I'm not sure there will be scientific evidence per se, since that would require experimental evidence. Instead, most of what I've seen about the golden ratio (or the associated logarithmic spiral or golden angle) are observational reports. The significance of this number is debated, but I don't see any arguments discounting its existence. –  leonardo May 3 at 18:46

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