[pct-l] GPS and Pi

[SnoLepard at TrekkingKats.com (SnoLepard)]

I'd just like to chime in about wheeling trail mileages. It concerns the difference in distances wheeled on the outside of the curve and the inside of the curve.

Using pi the formula for the circumference of a circle is pi times the diameter. Therefore if there were a hypothetical trail around a mountain and the trail was a circle ten miles in diameter the trail would be 31.415 miles long. If two hikers were to walk abreast at 3 feet from center of hiker to center of hiker, the hiker on the outside would hike less than 19 feet farther than the inside hiker over the entire loop trail.

Why is this? Because the diameter of the inside trail is 52800 feet and the diameter of the outside trail is 52806 feet, only six feet farther out. Two times the three foot difference. Multiply 52800 by pi and get 165,876.09 feet. Multiply 52806 by pi and get 165,894.94 feet. The difference is 18.849 feet.

Even if two hikers walked around the Earth at the equator, one on the ground and one on a wall three feet high, the hiker on the wall would still only hike 19 feet farther.