Are there special constants in biology that define organism's morphology?
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.