At 08:42 AM 4/8/98 -0400, you wrote:
>Brad,
>I count 24. It is unclear to me from viewing your link why they are
>talking about 27.
>
>First I thought this quote contained a typo: "Arthur Cayley's
>hyperdimensional geometry (the "27 lines on the general cubic surface"
>problem -- see diagram, right);"
Yes, it is definitly not a typo.
>
>Yep only 24 major lines unless you just count segments then there's 42.
>So the diagram doesn't seem to help. Is this some classical puzzle that
>we haven't heard of?
That is why I'm asking the question. I would like to know what the puzzle is.
>
>Now in some metaphysical doctrines, the numerology of threes and nines
>has symbolical significance. Maybe thats the tie-in. 3^3 is 27. Three or
>(3^1) is the minumum number of points needed to define a plane surface.
>A surface squared becomes a 3d volume. Raise that 3d to the next
>dimension and I guess we have the 4rth dimension or hyperspace?
I see what you are getting at. But, it says "27 lines on the general cubic
surface". So, just dealing with a 3d cube, where are the other 3 lines?
Maybe, joining the centre of each surface with its opposite side would give
3 more lines, but they are not on the surface.
I wish I could think more laterally!
Cheers,
Brad
Dr Bradley W. Scott
Saltbush Software
Agricultural Business Research Institute
University of New England, NSW
Australia, 2350.
Ph: +61 2 6773 5252
email: brad@saltbush.une.edu.au
Any intelligent fool can make things bigger, more
complex and more violent. It takes a touch of genius
and a lot of courage to move in the opposite direction.
-- Albert Einstein