quote:
I gave the answer to the problem Seutter proposed, not to the problem he didn't propose.
You are right, The answer you gave was for the theoretical rectangle. It's just that the math problem seemed ripe for further extrapolation, to see what the limits on the errors were.
From the extreme snaked road case, it appears clear that midline method is not just a little wacky, but totally devoid of any reasonable precision... 1,817 meters in a 5K.
Even with a simple rectangle they end up with an unacceptable error, as you point out.
Regarding his other example, an oval. Since I don’t know the dimensions, I used a classic case, the circle. With a circle, the error on a 10 lap course would be about 314.2 meters. Similar to the 295 meters in your solution but interesting because by rounding out the 90 degree turns into a circle it adds more error, not less. Not what I would have expected.