Because the surface of the Earth is irregular and complex, geodesists use simplified mathematical models of the Earth for many applications. The simplest model of the Earth is a sphere. A much more complex model of the Earth is the geoid, used to approximate mean sea level. Even the geoid is a simplified model, however, when compared to actual topographic relief, as shown in this image of four figures of the Earth (Grand Canyon).

Four figures of the Earth (Grand Canyon)

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