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Cahill Butterfly Map 1909
Cahill 1909
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Cahill-Keyes M-layout world map silhouette including Antarctica
Cahill-Keyes 1975

The Cahill-Keyes "Real-World" Map

Below is a reduced preliminary draft printed in 1984:

Click here for a bigger: 1/100,000,000 version (40 cm wide or 16") (715 kb).

Click here for photos of much bigger 1/20,000,000 (and 1/1,000,000) prototypes with one-degree geocells.

Actual scale of original digital image is 1/200 million. But see note below.

Cahill-Keyes "Real-World" Map
0 km
0 mm

20,000 km
100 mm

40,000 km
200 mm

[Note: first line of bar scale above is constant; second line is variable. See below.]

c. 1975, 1980, 2006, 2009 by Gene Keyes
cc logo
cc. 2010 for fair usage

Both online versions are replicas of an existing 1/20,000,000 "Jr. Master" wall map 2 meters wide, and an exact floor plan of a proposed 1/1,000,000 "Mega-map" with sides 40 meters or 132' wide.

This map is adapted from the B.J.S. Cahill octahedral "Butterfly" projection, published in 1909. The graticule was newly devised, computed, and drawn by Gene Keyes in 1975, along with the coastlines, boundaries, and overall map design.

1975-11-11, original GK version
1980-05-02, first print
1984-02-15, second print
2006-04-22, first online posting
2009-03-22, re-formatted online posting

Scale adjustment for varying computer screens:

Your mileage may vary! Monitor size and settings make a difference. If the distance between the outer tics is 200 mm, then the map depicted is 1/200 million, as in its "original". In any event, the span shown is 40,000 km, representing the unfurled circumference of the earth.

This HTML web page and map jpeg were originally produced on a Mac G3 and a 19" LCD monitor with a resolution of 1024 x 768, + 75 hz. If you want the real scale as seen on your screen, measure the distance in millimeters (which is variable) between the first 2 numbered tics, then divide that into the kilometer distance (which is constant) at the middle tic, and add the term "million".* For example, on my 17" monitor hooked to a Linux Asus eee 701 with the same resolution, the midpoint distance is 89 mm, not 100, as in my "original". Dividing 89 into 20,000 indicates that on that monitor the scale is 1/225 million, not 1/200 million. See also my "Notes on Scaling Cahill and Cahill-Keyes Maps".

* The above division is a shortcut, to avoid entering a lot of zeroes in a calculator, and we take a readout of, say, 224.7.... as the fraction 1/225 million.

Metrically, the earth's circumference is approximately 40,000 kilometers, or 40,000,000,000 millimeters (forty billion), there being 1,000 millimeters in a meter, 1,000 meters in a kilometer, and 1,000,000 millimeters in a kilometer.

So if we have a [Cahill-Keyes] world map that is 200 millimeters long, equatorially, and the equator being 40,000,000,000 millimeters around, we make a fraction of

200 mm
40,000,000,000 mm

knock off a couple of zeros:

2 mm
400,000,000 mm


1 mm
200,000,000 mm

and get the scale of 1/200,000,000. (Representative Fraction.)

Which is also to say:

Each millimeter on the map represents 200,000,000 millimeters on the ground.

Or, knocking off six zeroes to convert to kilometers, 200, we say that each millimeter on this map represents 200 kilometers on the ground.

Or, if your computer has made this map somewhat smaller than the original, as in my example above, then each millimeter represents 225 kilometers, not 200.

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