Why is it difficult to show the carved surface
of the Earth flat map correcty?
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To understand why, think of a globe. A globe is a spherical copy of Earth. It shows the shapes of continents and islands. It also shows the location of cities.
Now, suppose the globe is cut in half. Then, suppose each half is flattened out into a map. Now, all the shapes are distorted. Things no longer appear as they really are. Relative sizes, shapes, and locations have changed.
Every map has some sort of distortion. The larger the area covered, the greater the distortion. Size, shape, and distance can be measured accurately on Earth. However, they cannot all be shown correctly on a map at the same time. For example, a map can keep the correct sizes of land masses. It can keep the correct shapes of very small areas. It cannot keep both, though.
refer the pic attached. it shows how an accurate representation woul look like