Re: Enigma 1532 - Just reflecting

Jake wrote :
On Mar 31, 4:28 pm, Jake <derpif...@xxxxxxxxx> wrote:
....
On Mar 30, 11:21 pm, Chappy <petergregorychap...@xxxxxxxxxxx> wrote:
six mirrors vertically to form a regular hexagon with small
gaps between the mirrors.  Through one gap he shone a
laser beam ...  so that it emerged from the [opposite]
gap, after being reflected just once by all six mirrors.

Maybe another puzzle here, for which n does there exist the same
sort of solution for an n-gon instead of a hexagon?

...

Here are a couple of pictures for the pentagon:
http://img410.imageshack.us/img410/236/picsdt.jpg
http://img144.imageshack.us/img144/4383/pic2b.jpg


I probably should have explained at least a little bit: ...
The picture is probably still confusing.

Hi,

I was not able to see anything in your drawing. Because pentagons
overlap, it is too much confusing to show different paths in the same
diagram. Also plain coloring doesn't help... it hides "the black
lines" for instance !

Here are three different valid paths in pentagons
(that is reflected once in each mirror).

<http://cjoint.com/?edawFNouQT>

Two different paths entering 1 and exiting 3 ("opposite")
And another path entering 1 exiting 2 ("adjacent")

I didn't search exhaustively all possible paths.

There's a similar picture for hexagons, if you had colored the whole
edges instead of just a few points ...
but some of the edges will be half one color and half another.

That's why I didn't colour the edges : the colour depends on the path
to hit this edge !

Can I ask what program you used to generate your diagrams,

I used an old drawing program I have (GraphicWorks for Windows).
It has a tool to draw n-gons for any n, and a tool to reflect
the selected object(s) through a selected line.
The rest is repeating the reflection as much as required.

For a single path the colouring is automatically tracked by
the reflections in the program.
For a full tiling with hexagons, I had to cancel the colouring
and do it by hand, for the edges don't have only one colour, as
explained above.

Regards

--
Philippe Ch., mail : chephip+news@xxxxxxx
site : http://mathafou.free.fr/ (recreational mathematics)


.

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