the Planck constants
The Planck constants define the boundaries of the coherent bases of atomic logic. Here we showcase their phase plots, 2D and 3D surface plots, and their closed-form definitions.
Phase plots
Planck time
Planck length
Planck charge
Planck temperature
Planck mass
Surface plots
2D|3D
real|imaginary
Coherent closed-form definitions
Where 
= Archimedes' constant, 
= the imaginary unit, 
= Euler's number, 
= the Weierstrass constant, 
= the hyperbolic sine function, and 
= the cosine function.
The decimal values of these closed forms yield numeric values for the Planck boundaries to any precision:
= 5.39125836832313 ... × 10−44 sPlanck time
= 1.61625918175645 ... × 10−35 mPlanck length
= 1.87554596713962 ... × 10−18 CPlanck charge
= 1.41678698590795 ... × 1032 KPlanck temperature
= 2.17642683817579 ... × 10−8 kgPlanck mass