[r-t] Smith's Theorem

Robin Woolley robin at robinw.org.uk
Thu Sep 21 10:04:24 UTC 2017

Hi All,

The silence has been deafening since I posted the proof. Wasn't it easy? 
I don't think it contains any algebra beyond the sixth-form.

As a corollary, isn't the order of the false lead equal to the order of 
the transposition?

Remember, in June, ago I asked about Roncobello Place. This fails the 
test the theorem so cannot have extents with l/end calls. You will 
remember that the extent was obtained by splicing with symmetric f/wk 
version as the 'call'. In the same way, the half-extent of Grandsire 5 
can be considered as a splice with a symmetric method with p.n. 
& There is often more than one way of thinking of things - 
especially with Doubles methods. Whether one or another way is better 
depends usually on what you're trying to do.

On another matter, there was some discussion about the composition at 
p88 of the diary by RRH & DGH - which we now know to be by David W 
Beard. Someone disparaged the composition. However, I believe this 
disparagement to be mis-guided. The really interesting thing about the 
composition is that it is the only one which has a 'plain non-round 
7-lead course' which fits these (Horton's Four) method groups. I have 
checked this several times from my spread-sheet but will do so again. 
(Remember - calls only allowed at the course-end.) Like all things, 
finding the call-structures is the 'hard' part - fitting the methods is 
trivial (comparatively).

Best wishes

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