I was playing around with the antipodes map the other day, and this question came to me. Given that about 70% of the earth’s surface is water, and that there is more land surface in the northern hemisphere, I expect that the percentage isn’t high, but can anyone put a number to it?
If you draw an antipodal map this way, rather than using an interactive point locator like you were probably playing with, you can get a good idea:
http://bartonhome.ca/antipodal_map.png
What percentage is brown, representing the bits that overlap? I’m eyeballing it as about 24%. South America is about 12% of the Earth’s land surface, and it looks like the other bits are enough to finish filling up SA. Remember that Greenland is distorted by the projection.
In fact, I’m adjusting my guess down a little, because of the distortion of Greenland. Say 22-23%.
Fun!
The brown percentage would be easy to derive: just let the computer count colored pixels. As you imply, however, it would be better to start with equal-area projection. Maybe I’ll try that for fun.
A fun puzzle I worked on once is to find eight vertices of a cube on the Earth’s surface, where each vertex is on land. Or, easier, the four vertices of a tetrahedron.
You need an equarectangular projection… look at Japan in the linked png - it is different in place vs the one shown in the South America overlap.
Here’s another map:
Given the distortion at the poles, I’m guessing less than 5%.
I realize something like the equal-area Goode homolosine projection would be very difficult to work with, but wouldn’t any equal-area projection with adequate mathematical regularity work OK, assuming I map antipodes correctly? (I won’t try to define “adequate mathematical regularity”, but think it’s weaker than equarectangular.)
The linked image must have had its antipodes miscalculated. But I think that calculation should be easy on any equal-area projection “with adequate regularity.”
I’d like to start with a big map (i.e., many pixels), perhaps this cylindrical equal-area map. It’s Jpeg, which is inconvenient (best would be only 2 colors: blue and brown!), but I think I can fix that in about an hour.
I read some article years ago, musing about this subject. He author was impressed with how neatly the continents seem to fit into their antipodal oceans (S. America excepted): N. America into the Indian Ocean, Australian into the N. Atlantic, Asia into the S. Pacific, and Antarctica into the Arctic Ocean.
'Netting around I found this, probably as good as I would have done. The guy claims “5.17% land-to-land diameters”, but he admits to missing some water, so the correct figure is probably slightly less than 5%.
David Brin didn’t happen to give you this puzzle, did he? Part of his novel Earth involves setting up scientific stations on the Earth that are arranged in a cube; IIRC, in the novel some of the locations required are politically unfeasible, so they go with a tetrahedron instead.
Actually, the equator goes through the mouth of the Amazon in South America. I would think that you need to adjust the maps so the equator on each map line up. One map is a bit too high for the other. It looks OK longitude-wise, with the Alaska-Siberia gap of the Bering straight about even with Greenwich.
Then you can adjust for the mercator distortion.
Just by stats, the odds that 1/4 lines up with 1/4 is about 1/16.
Are you giving percentage of the Earth’s total surface, or percentage of the land area? The OP asked for the latter, which is what I was estimating above.
Which means the actual land-to-land antipodal points are far fewer than would be expected by chance, e.g. one of those randomly-generated continent world maps in the Civilization game having 24% land surface. Although I don’t know how to calculate how much that would be.
Oops. In that case my quote should have been 17%. But I’d better double-check the whole thing. :dubious: (I’ve been blundering dazedly lately – can no longer blame it on brain damage since I just had a clean CT brain scan. 
)
Thought of it myself about 6 years ago. … But was probably reacting to a subconsciously-remembered puzzle years earlier, perhaps by David Brin.
(By the way for geometry puzzlers, the 8 vertices of a cube are not the solution to “place 8 points on a sphere maximizing smallest point-to-point distance.”)
Nat’l Geographic had a 1-page article about this very thing. It’s maps (2 hemisperical ones with antipodals overlaid in gray) indicated a very small of land-land antipodal amount. 5% sounds about right.
Covered in “Right Beneath Your Feet” by I. Asimov. The Magazine of Fantasy and Science Fiction (Jan. 1967) collected in Science, Numbers, and I (1968).
I have this but not nearby. Anyone want me to dig it out? I’ll need an incentive.
Is our respect and gratitude insufficient?
I read that many years ago. It was written during the Vietnam War. I remember Asimov saying that if anybody wanted to get as far away from Vietnam as possible, that would be the antipodes in Ecuador. A subtle antiwar message.
I question the validity of that map (or my interpretation of antipodal).
[ul]
[li]On one side, Lake Baikal is antipodal with portions of South America. On the other side, Lake Baikal is in the Pacific Ocean off the coast of Chile. [/li][li]The antipodal of Hawaii is in a portion of Africa which, like Hawaii, is in the northern hemisphere.[/li][/ul]
Yeah, I was just going to say something is screwy there. Australia’s antipodal shadow is way too far north for a start.