NavList:

Bill Lionheart

An equilateral cocked hat with PLs from three equidistant sources 120 degrees apart must be every navigator’s dream.  In that case the incenter, centroid, and symmedian point would all be in the same place.  An interesting exercise on graph paper would be to take an equilateral triangle ABC and draw a line through C from the mid point of side AB.  Then move C backwards and forwards along that line to make a number of isosceles triangles.  Then note how the position of each of the new symmedian points moves with respect to the original centre point.  Would they move away from line AB, towards it, or stop the same distance away.  E.g. you might think that as C moves towards AB, the new SP must move towards AB, but AB is now the longest side, so how do you cope with that.  Similarly, as C moves away from AB, AB is now the shortest side, but the triangle is bigger.  It gives you a headache.  Fortunately, I’ve run out of A4 1/10” graph paper to try it.  DaveP