No flat map of the Earth can be perfect. But flat maps are easy to store and manufacture and are therefore desirable. Previously, Goldberg and I identified six critical error types a flat map can have: local shapes, areas, distances, flexion bending , skewness lopsidedness and boundary cuts. These are illustrated by the famous Mercator projection , the base template for Google maps. It has perfect local shapes but is bad at depicting areas.
Greenland appears as large as South America even though it covers only one seventh the area on the globe. A pilot flying a great circle route straight from New York to Tokyo passes over northern Alaska.
His route looks bent on a Mercator map—a flexion error. North America is lopsided to the north: Canada is bigger than it should be, and Mexico is too small. All these errors are important. Ignoring one of them can lead you to bad-looking maps no one would prefer.
The object here is to find map projections that minimize the sum of the squares of the errors—a technique that dates back to the mathematician Carl Friedrich Gauss.
The Goldberg-Gott error score sum of squares of the six normalized individual error terms for the Mercator projection is 8. The lower the score, the smaller the errors and the better the map. A globe of the Earth would have an error score of 0. We found that the best previously known flat map projection for the globe is the Winkel tripel used by the National Geographic Society, with an error score of 4.
It has straight pole lines top and bottom with bulging left and right margins marking its degree boundary cut in the middle of the Pacific. We seem to be reaching a limit on improving the Winkel tripel. When that occurs in science, one often needs a breakthrough, some out-of-the-box thinking, to make any radical progress. I realized I could make a back-to-back circular map: like an old-fashioned phonograph record. And while the general shape of the continents is maintained, you will notice that their orientation is skewing upwards — as if in a smile!
This is just popular bollocks. The distortion on Brazil is horrible. Lambert cylindrical projection has existed since the s! Gall—Peters is just one of the many vertically stretched variations. I find it more comprehensible then the AuthaGraph. It, too, is severely east-west compressed.
Also, Robinson designed his map to not greatly magnify the Arctic. Yes, Robinson flattens the Arctic a lot, but Robinson must have felt, and I agree, that a more accurate size for the Arctic is more important than accurate shapes for regions there. Winkel uses extreme horizontal compression to reduce that flattening, thereby making the Arctic more unrealistically large, and making the entire rest of the world too east-west compressed.
You said that Winkel scored best in a ratings-study that measured distortions. RMS preferentially fixes the biggest errors. With a flat pole, the Arctic ordinarily has the biggest errors. So, being more sensitive Arctic flattening, the rating-program favored the Arctic, and gave top rating to a map that east-west squashes the rest of the Earth to improve shapes in the Arctic.
More recently, […]. It provides the same correction to the shape of history that an alternative projection gives to the distortions taught to us by the Mercator of school atlases. The holographic map is the only map that resolves all information correctly into a functional map giving accuracy from any point of view chosen. Save my name, email, and website in this browser for the next time I comment.
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One confusing item is that these grid cells are variably called a UTM zone. As is explained in the section tiled Explaining Some Jargon — Graticules and Grids there is a significant difference between the two. This is not true of a graticule system! Therefore it is easy to measure distances using a grid — it removes the foibles of distortions inherent in each map projection.
This involves a regular and complex system of letters to identify grid cells. To identify individual features or locations distances are first measured from the west to the feature and then measured from the south to the feature. The three are combined to give a precise location — based on the map grid. This is a mathematically simple projection. It is also an ancient projection possibly developed by Marinus of Tyre in Because of its simplicity it was commonly used in the past before computers allowed for very complex calculations and it has been adopted as the projection of choice for use in computer mapping applications — notably Geographic Information Systems GIS and on web pages.
Also, again because of its simplicity, it is equally able to be used with world and regional maps. In GIS operations this projection is commonly referred to as Geographicals. This is a cylindrical projection, with the Equator as its Standard Parallel. The difference with this projection is that the latitude and longitude lines intersect to form regularly sized squares. By way of comparison, in the Mercator and Robinson projections they form irregularly sized rectangles.
Refer to the section on Projections for more information about distortions generated by projections. Enter your Keywords. Commonly Used Map Projections. Breadcrumb Home Fundamentals of Mapping Projections. These are two examples of maps using Stereographic projection over polar areas. In these the radiating lines are Great Circles. Produced Using G. In this the Great Circles are not as obvious as with the two Polar maps above, but the same principle applies: any straight line which runs through the centre point is a Great Circle.
This is an example of how a Great Circle does not have to be a set line of Longitude of Latitude. These two maps highlight the importance of selecting your Standard Parallel s carefully. For the first one the Standard Parallels are in the North and for the second they are in the South.
The Lambert Conformal Conic is the preferred projection for regional maps in mid-latitudes. Compare this to the Mercator projection map above.
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