On Sat, 27 Jun 1998, Antreas P. Hatzipolakis wrote:
[Conway]: > >> G.B.Trustrum and I proved that the answer lies between two > >>constant multiples of log n. The first interesting case is > >>n = 13, f(n) = 11 I think. Another nice one is n = 41.
[Antreas]: > >Question: Does anyone know the reference of the above proof?
[Antreas, later]: > Conway, J. H.: Mrs. Perkins's Quilt. [PCPS] 363-368, 1964. > Trustrum, G. B. : Mrs. Perkins's Quilt. [PCPS] 7-11, 1965. > (I was looking for a joint paper)
[Conway, now]: I see that my sentence inadvertently conveys that impression - sorry! My paper (which was the first I wrote!) established the lower bound, Trustrum's the upper one.
[Antreas]: > >1. Who invented the term "monostatic"?
[Conway]: I cannot tell a lie ... Well, actually I can. Out of sheer naughtiness I actually introduced two terms here, namely the macaronic words "unistatic" and "monostable", (which I think I gave slightly different technical meanings) but Richard Guy couldn't take this, and properly insisted on "monostatic".
[Antreas]: > My question actually is: who introduced in geometry the (well known otherwise) > term: monostatic. [Conway]: I disagree that it's "well-known otherwise", and doubt if any dictionary contains it. I see that the OED has "monostable" (hiss!) as a technical term in electronics. So I claim the moral credit for the geometrical term (my teasing of Guy being just in fun).
> R. J. M. Dawson proved that no monostatic simplex exists in <=6 dimensions > (He has found one in the dimension 10)
Before this I found that a tetrahedron could be monostatic if made of suitably non-uniform material, and also the enneakaidecahedron below ...
> R. K. Guy has constructed a monostatic enneakaidecahedron (it's a prism > with 17 sides [19 faces])
.... Guy was really describing my work. However, I have a feeling that we got both the problem and the idea for its solution from someone else (whose name I'm desperately trying to remember), and merely tightened everything up to get as small an example as we could. I have since had an idea that might reduce it a bit more, but have never troubled to work it out.
> >2. Reference of the above theorem?
I'm afraid I don't know. Doesn't Dawson give it? He was a graduate student at Cambridge and so knew both Guy and me (since Guy used to visit Cambridge fairly often). If your information stems from his paper, and that gives no reference, it quite possibly means that it was never actually published.