Hemispheres and great circles

ENGLISH ONLY auto-stripped version of
Chinese+English version.

I'm sure the reader can apply this to where s/he lives. (Great circles are of course tracks on the earth that take one to the exact other side of the world (antipode) and back.)

Half the world away from Taiwan

Closeups of the line demarcating the near and far hemispheres from Taiwan (and of course also from Paraguay). ( Source code) Same as the red great circle below.

near/far hemispheres: NW USA near/far hemispheres: Europe near/far hemispheres: East Africa We also graze along Antarctica's Wilkes Land coast, putting Antarctica just inside the far hemisphere. See the red circle below.

Great circles through Taiwan

Some interesting great circles passing thru Taiwan (and of course Paraguay), by azimuth, with points from west to east from Taiwan:

Azimuth	Great circle thru
24	Korea; near Bering Strait; along Florida Peninsula.
31.5	Canada's BC/Alberta border along Continental Divide (except most southern portion)
34	Strait of Korea, tips of Hokkaido, Sakhalin, Alaska, Yucatan, Honduras; Panama
50	Tokyo; Baja California: just skims North American continent; Cambodia
60	South edges of South Africa and Madagascar
74	Honolulu; Sri Lanka
93	Mouth of Congo River; Horn of Africa; northern extreme of Bay of Bengal
141	Between main New Zealand islands; farthest point in Europe: Portugal; Moscow
147	Queensland coast; English Channel; St. Petersburg, Russia
160	Tasmania, northern extreme of Norway and also thus Europe.

great circles depicted as spokes

( source code). Perpendicular to these are equidistant small circles

We might now make a pie chart on the floor for directions that each continent occupies, knowing their bounding edges' azimuths.

Wettest and driest great circles passing thru Taiwan

You announce you will travel a great circle, by foot. Your roommate announces he will travel a great circle, by boat. How to compute the great circle passing thru your house, that is the most land covering, and the other great circle which is the most water covering? ( source code)

Wettest and driest great circles thru Taiwan (and Paraguay):

Azm   Dry%
 59.2 10.97
175.9 51.50

wettest and driest great circles thru Taiwan

In this graph of azimuth vs. % dry land, we notice that azimuths thru Europe were close runners up for dry land.

World's wettest and driest great circles

We find the two great circles, not just passing thru Taiwan, but for the whole world, with the most land, and the most water.

wettest and driest great circles in the world

Our crude program finds two wettest circles, skirting Africa, with 8% land, and one driest circle, thru Antarctica, with 55% land. I have superimposed tracks from several runs. I'll leave finding the exact winners to the pros.

Land hemisphere, water hemisphere

Also note people have calculated the land hemisphere and water hemisphere. One could also make a "people hemisphere", where most people live, etc. Maybe all this splitting things up isn't very meaningful...

Hemispheres of Control for world dominance

I live in Taiwan, my little brother, say, lives in Sweden. I want to divide up the world into hemispheres of control. Muhahahaha.

Dividing the world with little brother

The black great circle divides our hemispheres of control for world dominance, simply showing the "closest police station (brother) to any trouble site". The red and green great circles delimit what is more than "half a world away" from each one of us. No more casual use of that phrase allowed!

For a meeting with little brother we chose the best place (midpoint of great circle thru us), and worst place (other midpoint of said circle), antipode of first.

To do:

Redivide to give Mom who lives in Chicago an equal slice. (But see below.)
Best and worse meeting places for us three.
Extend the program to allow any number of participants. Wait: the equal slice idea breaks down as can be seen by a circle of friends with one in the middle: there is no way for him to have an equal sized area of the world that he is the nearest one to. Indeed, with three friends in a row, the middle one only gets a narrow band that he is the nearest one to, eh?
Well, at least I can compute the best point for a group of friends to meet, just average their longitudes and latitudes? No, wrong, as seen even in our two person image.

Sorry Mom, Ben Horner-Johnson deserves the next slice, as he wrote the whole program for me, using GMT. You see, my personal head is all bubbles. The most I can do is "frame the problem". I'm grateful that there are folks who have implemented it for me.

Look! my page was actually read, by scientists none the less, 6/2002:

Mark.Fenbers at noaa.gov: I like it! I bookmarked the page!
R. P. Channing Rodgers, M.D. at nlm.nih.gov: Yes, very nice! I would point out that the "Worst Meeting" p point is bad in more than one respect -- it also happens to be under water! :)
To which I say: If that were a concern we wouldn't have straight boundaries in the first place. We use spacemobiles.
2002.6.9 Robert Israel in news:sci.geo.cartography said: The points equidistant from A and B form a great circle, as do the points equidistant from B and C. The intersections of these great circles are equidistant from all three.

Center of population of the world

Certainly someone has already done this. Perhaps have an XYZ coordinate system centered at the center of earth. Now just average the X,Y,Z of each person: (sum of X,sum of Y,sum of Z)/population of the earth

This will give a point say near China or India but very deep within the earth. Now just project upwards to the surface, and voila, your McDonald's franchise location expert choice is ready. Perhaps somebody would like to take a whack at it using the "Gridded Population of the World (GPW) dataset". Anyways, perhaps the result isn't very meaningful...

Etc.

Projects one can do: find if there are any great circles on which you live on their highest point.

Dan Jacobson

Last modified: 2006-07-05 07:44:23 +0800