On Sun, 21 Aug 2011 09:44:08 -0700 (PDT), Hoosierpopi
wrote:

On Aug 20, 8:02*pm, whit3rd wrote:
It's the compass-and-straightedge method

I recall reading somewhere that you could accomplish this task w/o the
math. It involved drawing a line diagonally through the rectangular
area intended to receive the holes. It was explaining, as I recall,
how to evenly space shelf support pin holes on the interior sides of a
bookshelf.

As I recall. you measured the resulting line and divided it in half at
the middle, then repeated this with the resulting segments on either
side (marking the "center points" as you went along. Then, taking a
square to the edge of the board and through each point along the
diagonal line, made a hash mark at the center of the board. Each of
these would, then be the center of your evenly-spaced holes.

Anyone know of something like this (recalling it from distant memory).

That works for certain number of holes (2^n-1) holes but not for an arbitrary
number of holes. The OP wants six holes.

This problem is essentially the "trisecting the angle" geometry problem, which
has no solution (bisection is possible, but an arbitrary number is not).