The irrational number π plays an important role in geometry and trigonometry. It also appears in the expressions of some fundamental physical quantities and equations, such as in the expression of the period of a pendulum or in the value of the reduced Planck’s constant. Here, I show that the speed of light in free space can be expressed in terms of a power of π.

The wave equation, for the electric field component of an EM wave propagating in free space, can be written as:

∇²E – µ₀ϵ₀ ∂² E/∂t² = 0¹

µ₀ϵ₀ = 1/C₀²

where the permittivity of free space is given by ϵ₀ = 8.854 10^-12 F/m, and the permeability by µ₀ = 4π 10^-7 H/m.

C₀ is the speed of light in free space, which equals, if we round up to the third decimal, to 2.998 x 10⁸ m/s. This number, 2.998 x 10⁸, is approximately equal to π¹⁷ and exactly equal to 1.06 x π¹⁷ when rounded up to the third decimal.

Currently there is no known physical law to directly relate the speed of light in free space to the number π. However, the fact that the value of C₀ can be expressed as a power of π, may be of interest to mathematicians and mathematical physicists. In addition, note that π is elevated to the power of a prime number (17), which itself is composed to two prime numbers, 1 and 7, which when added together (1 + 7 = 8), is exactly the power of ten in the numerical expression of C₀ (i.e. 10⁸). Again, these are just number plays, not backed up by a specific theory.

Dr. Mounir Laroussi, Old Dominion University, is a NPSS Distinguished Lecturer. He can be reached at [email protected].