Here's a diagram to better visualize the relationships.
Drawn in Visio 2007

7 hexagons, rotated -40.9801 deg.

Left line resulting angle was 19.0199 deg.


Oh, also:
http://logo.twentygototen.org/mJjiNzK0
has
"make "ln :ln / 2.6457" as part of the construct.   I'm not sure if that has
anything to do with your magic number for L.

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