for those who think Descartes was a fool .... A boat sails 200 miles west, then 200 miles north, then 200 miles east, and finally 200 miles south. Does it end up at the same spot it began its journey? * * The answer, of course, is not. But why not?
I should hope so. But, if not, why not? I'm sure Descartes would have been worried about whether he was really in the boat or whether some Cartesian evil genius had fooled him by causing some sort of projection of him to seem to be sailing in an imaginary boat. But, what's the real answer? Do praytell, please.
I'm just going to guess and say, "Because the boat is traveling along the arcs of the Great Circle, and not on a plane." Ian's answer being "Only if it started 100 miles south of the equator" being because if the boat crosses 100 miles at the equator, the effect of the great circle would have it traveling equal arcs in all distances in relation to the Earth's curve. But this is just a guess -- I've never been much of a traveler.
In Flatland he makes it home. Even the 100 miles south thing doesn't work perfectly, since the earth is not a perfect sphere. If you tell me that the distances are defined as in Riemannian geometry, then maybe we're back in business.
Yeah, you guys got it. The point is that the meridians are not parallel among themselves (as Ian said, at the equator they are probably parallel, at least, for short excursions of 100 miles around a point). So if you go north through a meridian, go west after through a parallel and then south again through another meridian, then you are more than 100 miles from the origin. The more to the north (or south) the more off course you would be. And at the equator you might be able to return to the origin. Unintelligible explanation that I am giving, but I am sure you know what I mean.
I am afraid I don´t understand you. OK, the earth is oblate, but if you travel south you go south without having that affected by the oblateness of the earht. Travelling south is possibly defined as following one of the infinite lines that join the most northern point of the earth with the most southern point of it. So even if the earth is not a perfect sphere, you still go perfectly south (what a mess ) Regards
Because of the oblateness of the earth, one hundred linear miles would probably translate to slightly different arc lengths as one travelled each side of the "square", even if one started 100 miles south of the equator.
Re: Re: another trivial pursuit type question Correct Semisopochnoi Island in Alaska is 179.6 degrees East longitude. http://volcano.und.nodak.edu/vwdocs/volc_images/north_america/alaska/semisopochnoi.html
