Napoleon's Theorem - Background

Background

The theorem has frequently been attributed to Napoléon but several papers have been written concerning this issue which cast doubt upon this assertion (see (Grünbaum 2012)).

The following entry appeared on page 47 in the Ladies' Diary of 1825. This is the earliest known reference to Napoléon's theorem, and it is to be noted that that name does not appear here.

VII. Quest.(1439); by Mr. W. Rutherford, Woodburn.

"Describe equilateral triangles (the vertices being either all outward or all inward) upon the three sides of any triangle ABC: then the lines which join the centres of gravity of those three equilateral triangles will constitute an equilateral triangle. Required a demonstration."

Since William Rutherford was a very capable mathematician, his motive for requesting a proof of a theorem that he could certainly have proved himself is unknown. Maybe he posed the question as a challenge to his peers, or perhaps he hoped that the responses would yield a more elegant solution.

Plainly there is no reference to Napoléon in either the question or the published responses, which appeared a year later in 1826, though the Editor evidently omitted some submissions. Also Rutherford himself does not appear amongst the named solvers. The first known reference to this result as Napoléon's theorem appears in Faifofer's 17th Edition of Elementi di Geometria published in 1911.