Based on the tunnel distance formula from Wikipedia, I calculate that the tunnel distance (shortest distance between two points on Earth's surface, straight through Earth, based on a spherical Earth) between the South Pole and a point 40 degrees north is about 90% that of the full diameter of Earth. I personally find that surprising. I believe the formula on Wikipedia is correct, both because I did a few sanity checks as well as found this answer with the same formula.
My question is, how can it be that a point which is so far still from the North Pole (it is closer to the equator than it is the North Pole) be almost as far away from the South Pole as the North Pole is? I believe my calculation, but the result is a bit surprising, and I have a superior who doesn't quite believe the result. How would I explain it to him? He is mathematically literate.
When I say 40 degrees north, I am talking about standard latitude and longitude, which is measured from the equator.