半球及大圓 Hemispheres and great circles

讀者應能應用至其所居之地方。 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.)

離台灣半個地球 Half the world away from Taiwan

沿著分開遠與近台灣的兩個半球的界線來選處放大 Closeups of the line demarcating the near and far hemispheres from Taiwan (and of course also from Paraguay). (原始碼 Source code) 同上圖紅大圓。 Same as the red great circle below.

亦沿著南極洲之威爾克斯地海岸線， 而該洲落於遠半球。 We also graze along Antarctica's Wilkes Land coast, putting Antarctica just inside the far hemisphere. 見上圖紅大圓 See the red circle below.

經台之大圓 Great circles through Taiwan

有趣經過台灣的大圓包括 Some interesting great circles passing through Taiwan (and of course Paraguay), 依方位角， 點從台灣由西往東而列 by azimuth, with points from west to east from Taiwan:

(原始碼 source code). 與之交叉有 Perpendicular to these are 等距環 equidistant small circles

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

經台灣最濕最乾大圓 Wettest and driest great circles passing through 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 through your house, that is the most land covering, and the other great circle which is the most water covering? (原始碼 source code)

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

Azm   Dry%
 59.2 10.97
175.9 51.50

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

世界最濕最乾大圓 World's wettest and driest great circles

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

兩最濕圈，一最乾圈 Our crude program finds two wettest circles, skirting Africa, with 8% land, and one driest circle, through Antarctica, with 55% land. I have superimposed tracks from several runs. I'll leave finding the exact winners to the pros.

陸半球， 水半球 Land hemisphere, water hemisphere

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

與弟瓜分地球 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. 我住台灣， 我弟弟假設住瑞典。 我想與他瓜分地球成兩個「控制區」一人一區， 以便控制世界， 嘻嘻嘻。

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! 從此不能輕易說某地離這兒「半個世界遠」， 今能看一清二楚。

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

To do:

1. Redivide to give Mom who lives in Chicago an equal slice. (But see below.)
2. Best and worse meeting places for us three.
3. 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?
4. 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...

其他 Etc.

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

Update 2010/7: I must have been a pretty smart "M.F." when I wrote this back in 2006. A math whiz compared to now, as I reach for the Geritol™. However I didn't know how to spell 'through'.

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Last modified: 2015-09-14 15:47:02 +0800