What is the simplest mathematical representation of Earth?

The sphere is the simplest mathematical representation of Earth due to its uniform curvature and symmetrical properties. This model assumes that the Earth is a perfect sphere, which simplifies calculations related to distance and area on its surface. While in reality, the Earth is not a perfect sphere but rather an oblate spheroid (slightly flattened at the poles and bulging at the equator), the sphere serves as an effective approximation for many geographical and astronomical applications.

This simplification allows for more straightforward calculations when modeling geographical phenomena, such as the layout of maps and the calculation of distances between points on the Earth’s surface. Additionally, many fundamental principles of GIS and spatial analysis commonly utilize the spherical model for ease of computation and conceptual understanding, even though more complex models exist for greater accuracy.