3 A flat map of a spherical world

A geography map is a two-dimensional depiction of the actual physics topography the a geographical region, and also whilst practically everyone is acquainted with, for example, a roadway map, mapping is a complex subject. The do of maps is referred to as cartography and fundamentally the is about the relationship between data (the details you wish to display and also convey) and also space. This is both the geographic space being represented and the room available ~ above a paper of file or screen screen. The data are represented by clues (to show location) and lines (to present connections or borders), by icons (to convey features), and finally by names and also colour and/or shading (to represent areas). The course, the names of places, like London, or contour lines representing height, nothing physically appear on the ground wherein they are displayed on maps!

One that the challenges facing cartographers as they shot to to express both data and space at the biggest scales (i.e. The whole earth or big sections the it) is the standard problem of representing functions on the curved surface ar of a spherical planet (or globe, see Figure 4) on a airplane (or flat) surface.

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Take an orange and draw the rundown of two shapes on that peel through a feel pen. ~ above one side draw a circle and on the various other a square, making certain your shapes cover at least a third of the surface ar of the orange. Now peel the orange, do the efforts to leaving the skin in one piece. Take her peel, and put some cuts in it at the edges with a knife or scissors so that it will lie completely flat ~ above a table.

Can you still check out your shapes with specifically the same summary as once you drew them?


Answer

You were asked to attract two large shapes so the you have the right to see the distortion. Relying on where you put your cut it is unlikely that your shapes will be specifically as girlfriend originally attracted them. In the run from 3 dimensions to two dimensions the shape has become distorted. The means this distortion is avoided is by making use of a map projection.


In your answer come Activity 2, whether you could see your shapes in the same way you attracted them counts on whereby you do the cuts. However it is feasible to do a flat illustration of the surface of the orange through your forms on to present them together you actually drew them. This is referred to as a map projection. All projections involve some sort of compromise since it is just not possible to store everything fully accurate when shifting from 3 dimensions come two. An example of a projection of map data is displayed in Figure 6a, which is the planet in what is referred to as the Lambert equal-area azimuthal projection. It is round like Figure 4 and you should be able to recognise some of the land forms in this map.


Is it feasible for girlfriend to organize an orange or apologize in such means that you deserve to see both poles as presented in Figure 6a?

No! You deserve to only watch the optimal or the bottom at one time.


What are the most distorted nations shown in number 6a?

Australia is fully unrecognisable in addition to the Pacific coastline of Russia and North America.


In Figure 6a, the lot of distortion changes with distance from the center of the map at 0° N 0° E. To show this, there space a number of circles overlain on the picture. Each one of the one encloses one equal surface ar area of the Earth. If friend think earlier to your orange, imagine spanning it with regularly spaced round stickers around 1 cm across. Every sticker would certainly cover the exact same surface area of the orange. However in the forecast in Figure 6a the dimension of the circles is varying – they are bigger the further away they room from the center of the map.


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Figure 6 2 projections of the Earth. (a) The Lambert equal-area azimuthal projection. (b) The Mercator projection. The circles enclose an same area of surface of the Earth.

If the circles show up larger however are in reality the very same size, what is happening come the surface area the they cover?

The surface area is being distorted ~ above the map so the it appears larger.


If there was no distortion in the projection, then every one of the circles would certainly be the same size anywhere the map.

A frequently used map estimate is the Mercator forecast (Figure 6b) and on it the lines of longitude and also latitude cross at ideal angles. This photo also has the same circles together Figure 6a i beg your pardon cover an same area.


How perform the circles change size relative to the Equator in the Mercator projection?

The circles space equal in size along present of latitude near the Equator however increase in dimension with distance from the Equator.


Based on the size of the circles, just how are Greenland and also Antarctica distorted by the Mercator projection relative to their actual size?

Because the circles are bigger towards the poles, the Mercator forecast shows Greenland and Antarctica as bigger than they have to be. Together there is no solitary point because that a pole, Antarctica is basically unrecognisable.


The Mercator projection is often used for maps through a small range of latitudes so there will certainly not be an extremely much distortion. When there is a big range the latitude favor in Figure 6b, that is not simple to recognize the family member sizes of various regions. There are many different projections and also it is important to store in psychic that all of them distort geographic data come a details extent. The an essential is to pick a estimate that distorts your geographic an ar of interest the least. This course is focused on the polar regions and for this reason you will typically encounter what is dubbed the stereographic projection (Figure 7a, b), which is indistinguishable to being over the North and also South Poles and looking downwards. The stereographic forecast is very great for mirroring the high latitudes as there is only far-reaching distortion at huge distances indigenous the poles.

Looking at the stereographic projection starting at the pole and also working outwards, the lines of same latitude room dotted and increasing in dimension (as shown in Figure 5). In Figure 7, the very first dotted circle is in ~ 75° north (or south) and also the second 60° north (or south). Lines of same longitude are just like hours on a clock, and are explained in Figure 5.

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Figure 7 The stereographic forecast of (a) the north Pole and also northern regions and (b) the south Pole, Antarctica and also the surrounding ocean.