A reminder of the powers of π

In a two-sentence Letter to the Editor of Physical Review, Friedrich Lenz made the noteworthy observation ¹ that the value of the ratio m_p/m_e could be expressed to all significant figures of the time by 6π⁵. That was in 1951, and remarkably, years later the observation holds true to good approximation. His note is perhaps also the shortest article ever published in Physical Review (27 words, 1 number, 1 equation, and 1 reference).

Its modern version could read as follows: The most exact value at present ² for the ratio of proton to electron mass is m_p/m_e = 1836.152 673 89(17). Despite years of experimental improvements, that number still coincides, to good approximation, with the simple, unambiguous representation 6π⁵.

With the 66th birthday of Lenz’s intriguing observation, it seems fitting to make his result better known to the community. This reminder should not be construed as trumpery—a showy but worthless statement—but as a comfort that some facts remain true with the passing of time.