It turns out that, geometrically, C is of course much closer to the mark than A or B, but that doesn't count, since no one can sail directly into the wind.

In fact, all the boats are equidistant from the mark, about 20 'blocks', as shown by the grid. Hence the cute name in Mathematics: we are measuring distances in 'city blocks', if you like. (We assume, for simplicity, that all boats can sail at exactly 45 degrees to the wind.) You could start at any position on this starting line, and you would be the same 'city blocks' distance, that is, sailing distance, from the mark as any other position.

Now let's look at the problem from a slightly different angle. Here we have four starting lines, each one showing some degree of bias.

Which of these starting lines, A, B, C, or D, is the 'fairest'? To keep it simple, let us assume that, by 'fair', we mean that you have an equal distance to sail to the mark whether you start at the port end of the line or from the starboard end. See what you think here.

2005-12-18

©2024 Lester Gilbert