Thursday, January 7, 2021

Gershon's Equation

 Today, I discovered the Association of Lunar and Planetary Observers, founded 1 March 1947 in Las Cruces, New Mexico. I had no idea that they exist, even though we  lived in Las Cruces for two years, and I worked with one of the founders, Walter Haas. Today, I joined.

On 1 December 2020, lining up on Mars, I saw a pair of stars that looked like a binary. I noted the time and their approximate position. Eta Piscium was discovered by S. W. Burnham in 1878.


"But Gershon, you can't call it Gershon's equation
 if everyone has known it for ages."
(Sidney Harris, What's So Funny About Science?)

It turns out that there is a Gershon's equation which "everyone" has known about for 700 years.

One year later [1322], at the request of the bishop of Meaux, he wrote The Harmony of Numbers in which he considers a problem of Philippe de Vitry involving so-called harmonic numbers, which have the form (2^m) * (3^n). The problem was to characterize all pairs of harmonic numbers differing by 1. Gersonides proved that there are only four such pairs: (1,2), (2,3), (3,4) and (8,9). --


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