Antipodes (opposite points on world's surface)

[Dave Simpson]

For those who are bored with nothing new lately on the Campaign Trail
2004, and who have an interest in geography, take a look at the
following. Beijing to Buenos Aires (or Shanghai to Buenos Aires)
would be a mighty long trip as well as interesting change of location.


Beautiful South America-East Asia superimposition (Zhanjiang-Iquique)

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Close-up example (South American nuke plants and the China syndrome)

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Larger-scale version

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The world

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Example geography-fan antipodal project

http://www.schneevongestern.net/jozwiak_org/1_0_docs/1_1_central_eng/top_eng.htm


Sadly, there's no place to relocate the United Nations antipodal to
this country. Antipodes Island would be a good choice for relocation,
though.

Antipodes Islands

http://encarta.msn.com/map_701510160/Antipodes_Islands.html

http://www.heritage-expeditions.com/index.cfm/Destinations/Sub%20Antarctic/Antipodes%20Island

home.att.net/~bpatftw/po12antip.htm

www.niwa.co.nz/pubs/wa/10-3/rockhopper1_large.jpg/view

[g***@internet.charitydays.uk.co]

Post by Dave Simpson
For those who are bored with nothing new lately on the Campaign Trail
2004, and who have an interest in geography, take a look at the
following. Beijing to Buenos Aires (or Shanghai to Buenos Aires)
would be a mighty long trip as well as interesting change of location.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
It's interesting how almost no land on the planet overlaps.

South America seems to be the exception.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Post by Dave Simpson
Beautiful South America-East Asia superimposition (Zhanjiang-Iquique)
http://jidanni.org/geo/antipodes/images/world.png
Close-up example (South American nuke plants and the China syndrome)
http://jidanni.org/geo/antipodes/images/tai_par_arg.png
Larger-scale version
http://jidanni.org/geo/antipodes/images/tai_par_arg_wide.png
The world
http://www.peakbagger.com/geog/worldrev.gif
http://www.wendycarlos.com/maps/nadirs.jpg
Example geography-fan antipodal project
http://www.schneevongestern.net/jozwiak_org/1_0_docs/1_1_central_eng/top_eng.htm
Sadly, there's no place to relocate the United Nations antipodal to
this country. Antipodes Island would be a good choice for relocation,
though.
Antipodes Islands
http://encarta.msn.com/map_701510160/Antipodes_Islands.html
http://www.heritage-expeditions.com/index.cfm/Destinations/Sub%20Antarctic/Antipodes%20Island
home.att.net/~bpatftw/po12antip.htm
www.niwa.co.nz/pubs/wa/10-3/rockhopper1_large.jpg/view

[Dave Simpson]

Post by g***@internet.charitydays.uk.co
It's interesting how almost no land on the planet overlaps.
South America seems to be the exception.

Yes, South America overlaps with parts of southeast and east Asia.
It really does make it possible for people at each of these two parts
of the world to be able to conceive of people also on land, on the
other side of the world. There is also enough overlap of various
latitudes that it involves seasonal as well as diurnal opposite
conditions. It's a fascinating intellectual or academic subject (and
a refreshing break from politics and grenade-throwing).

(Consider the two large, interesting,
always-a-potential-great-future but always problem-ridden, yet
developing, pair of nations that have similar reputations, and even
have both been involved in modernity such as with aviation projects:
Brasil and Indonesia. The two are roughly opposite each other in the
world.)

What is fun to do is to print out some of these maps with the
inverted views superimposed on the "normal" views of the world, in
monochrome (black and white -- the different colors in the original
come out to slightly different shades or thicknesses in monochrome
prints), and imagine how our history might be, as well as geography,
if we had twice the land areas on our planet's surface, and it was
this "mirror-image dual set" geography. (For example, the
well-traveled North Atlantic would feature a large "Ohio," an
upside-down Australia, right in the middle of it. Think of the
easier, much increased, trade and travel if that were so.)


Dave Simpson

[Baldin Pramer]

Post by Dave Simpson
For those who are bored with nothing new lately on the Campaign Trail
2004, and who have an interest in geography, take a look at the
following. Beijing to Buenos Aires (or Shanghai to Buenos Aires)
would be a mighty long trip as well as interesting change of location.

Interesting. Thanks.

An interesting thing about antipodes: it is possible to prove that there
exists on the earth at least one pair of antipodal points where the
temperature and barometric pressure are exactly the same.


Baldin

[Dave Simpson]

Post by Baldin Pramer
An interesting thing about antipodes: it is possible to prove that there
exists on the earth at least one pair of antipodal points where the
temperature and barometric pressure are exactly the same.

How is this proven?


Dave Simpson

[John Starrett]

Post by Dave Simpson

Post by Baldin Pramer
An interesting thing about antipodes: it is possible to prove that there
exists on the earth at least one pair of antipodal points where the
temperature and barometric pressure are exactly the same.

How is this proven?
Dave Simpson

I would have to think a little about the proof for two variables (temp
and pressure, for instance) but for one, say temperature, it is pretty
easy. Just restrict your function to a circle. Then when you prove it is
true on a circle, let that circle be a great circle on the earth and you
have it.

To prove it on a circle, take any continuous function on the circle. You
need to show that the function takes the same value at opposite points
on the circle. Cut the circle and its function and lay it flat. Then you
have a two dimensional graph with the circle as the x axis, where the
opposite ends are identified (they are to be considered connected). Lay
two of these graphs end to end (you'll see why in a second). Take a line
half as long as the circumference, and attach both ends to the graph.
Then move the line along, always keeping both ends on the graph. If the
line is ever parallel to the x axis (has zero slope), then the points on
the end have the same value, and because the line is half the
circumference, you have proved that antipodal points on a function on a
circle have the same value.

The proof: There are three possibilities.

1. The line is always parallel to the x axis. Then the function is
constant, and the proof is done.

2. The line always has a slope less than or greater than zero. Then the
function is always increasing or decreasing. But then the ends wouldn't
connect when the circle is reconnected, and the function is not
continuous, contrary to the assumption.

3. The slope changes from positive to negative or negative to positive
at some point. Then the slope had to go through zero, and the proof is done.

As to the two variable case, you would have to ask Baldin.