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);"
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?
But then obviously 27 is three times nine from the phrase
"...Ye cubic surfaces! By threes and nines, Draw round his camp your
seven-and-twenty lines- The seal of Solomon in three dimensions
[emphasis added].."
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?
-Gerald O'
Bradley Scott wrote:
> Hi All,
>
> Can someone please tell how do you count 27 lines on the surface of a cube?
> The most I can get is 24. Where are the other 3 lines?
>
> (see: http://www.enterprisemission.com/hyper1.html)
>
> 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