Three Countries in a Row:
The Final Jeopardy! clue a few weeks ago was the following:
On the Globe
Moving west from Canada, the next 3 countries through which the Arctic Circle passes
For the answer, click below:
(show)
My challenge for you is this: There is a place in the United States where, if you travel in a straight line in one of the four cardinal directions, the first three foreign countries you hit will all start with the same letter of the alphabet. Where is that place, what direction must you travel, and what are the three foreign countries?
To the East is Canada.
To the North is Canada.
To the South is Canada.
From Hawaii, I don't believe you can get to Mauritania without passing through either Cuba or Haiti/Dominican Republic. Could you provide a latitude at which this works?
From Miami, I don't believe you can pass through both Morocco and Mauritania. No part of Morocco seems to be west of any part of Mauritania. Again, could you provide a latitude?
I believe that all of the Caymans are east of Costa Rica, so you cannot go due south from one to the other. Again, could you provide a longitude?
On the "generous definition of the word south" suggestion:
Even if you were to keep following that line straight down through Antarctica and then come back up the other side, you wouldn't magically appear in Canada. You'd have to first come up through Asia, hitting approximately India or Bangladesh next.
Without that caveat, it won't work.
For a while, I thought you could avoid the Caymans and Haiti/Dominican Republic by using a lower latitude, but in fact if you go south far enough to avoid those countries, your route ends up passing through Belize (and maybe through one of the Antilles on the other side of the Caribbean).
Go south from Detroit, and you'll hit Canada, Cuba, and Costa Rica.
Any other alternative solutions are welcome.
Detroit's Wayne County Metropolitan Airport at 083° 20' 55" W. Then, a map of Costa Rica shows us that the southernmost border of the country is to the E of 082°. And this map of Cuba shows Castro's island to span from about 074° to pretty much 085° territory.
So, I'd say that 083° 20' 50" W would work just fine. (I guess no one needs evidence for Canada, right? hehe).
No, it's to the E of 83, not 82.
Nertheless, I think your answer is otherwise correct. Best I can estimate from my Natl. Geo. world atlas, a line straight south from Detroit misses the land mass of Honduras/Nicaraugua by about 10-15 miles, and runs into Costa Rica.
OK, I just proved it to myself. I put that marker at the center of the screen, and had Google Earth (a *very* cool tool, BTW) keep flying me south. Went through Canada, Cuba, missed Nicaragua/Guatemala's eastern edge, and landed in Costa Rica, right in the suburbs of Limon.
Case closed.
I think we may be able to find four inn a row through Canada, Cuba, Costa Rica, and Chile, though. There are a few off-shore islands that look to be right in the way.
Any access to Costa Rica is going to have trouble with the Nicaraguan offshore islands, though.
You might want to read the puzzle again....
Given this alternative interpretation, are there any other solutions?
I don't see how you reach that conclusion. In spherical geometry, lines of latitude, longitude, and great circle paths are all straight lines (or as straight as lines on a curved surface can be).
Why do you think that walking along the Arctic Circle does not trace a straight line, but walking along a great circil does?
Lines of latitude are not straight lines. If they were you could have more than one line defined by two points and all versions of non-Euclidean geometry prohibit that.
I guess really what is at issue here is the definition of "east". Not quite as bad as defining "is", but still. I see two different definitions. One is that east means progressing along a latitude line. The second one is to proceed in a direction orthogonal to the Great Circle formed by the two (actual) poles and the designated location (and the center of the Earth, hopefully). And proceeding orthoginal to this Great Circle would appear to be another Great Circle, and not the latitude line.
But, of course, this entire discussion of Great Circles ignores one of the simplifications that we invariably apply to this sort of thing. The Earth is, in fact, not a sphere, but rather is slightly flattened on top and bottom, bulging a bit in the center, presumably due to centripital force. So, in fact, the only actual Great Circle we have is the Equator. The rest are Great Elipses.
Latitude - "an imaginary line around the Earth parallel to the equator"
Longitude - "an imaginary great circle on the surface of the earth passing through the north and south poles at right angles to the equator; 'all points on the same meridian have the same longitude'"
Great Circle - "Circle formed by the intersection of a sphere and a plane that passes through the center of the sphere", but also "A line on the earth's surface, the plane of which passes through the centre of the globe. This shortest distance between two points on the sphere is also known as an orthodrome."
East - "the cardinal compass point that is at 90 degrees", but also "is the direction in which the Earth rotates about its axis"
Note that arguably the two different definitions of East here give two different results. The first would seem to describe a Great Circle, whereas the second, a line of latitude.
But we actually live on a planet that is typically simplified as being a sphere. And the geometry of the surface of a sphere is different - it is a non-Euclidian geometry. And there, the definition of orthoginal results in another Great Circle cutting the center of the sphere. But that means that it does not follow the latitude lines, but rather loops around the Earth dipping below the Equator on the other side the same distance that the subject point is above (or visa versa).
So, I would suggest that if you define East as being orthoginal to a line between the poles running through the subject location, it is a Great Circle. But the sun doesn't rise in that way. Rather, if you define the term based on the direction in which the sun rises, you would use latitude instead.
Here, the puzzle gave us certain parameters, specifically: "...travel in a straight line in one of the four cardinal directions...."
The puzzle thus inhabits a universe in which travel in any of the four cardinal directions is, by definition, travel along a straight line. Traveling east or west along a line of latitude, then, is by definition travel in a straight line--great circles be damned.
BTW, I understand that spherical directionality is a matter of hot debate in some Muslim circles (no pun intended). There are proponents of "facing" Mecca as defined by latitude and longitude from where one is (e.g., in Minnesota one would face roughly ESE), and equally insistent opponents who claim that the only true way is to use great circle routes (which in Minnesota would mean facing roughly NE).
Which is, I suppose, no more intrinsically peculiar a debate than Christians killing each other over whether the holy spirit proceeds from just the father, or from the father and the son (filioque), with 1000 years of schism resulting. Both of them strike me rather like flat-earthers arguing whether the flat earth is circular or square....