Spherical Earth

Belief in a flat Earth is found in humankind's oldest writings. In early Mesopotamian thought the world was portrayed as a flat disk floating in the ocean, and this forms the premise for early Greek maps like those of Anaximander and Hecataeus.

By classical times an alternate idea of a spherical Earth had appeared. This was espoused by Pythagoras apparently on aesthetic grounds, as he also held all other celestial bodies to be spherical. Aristotle provided physical evidence for the spherical earth:

Ships receding over the horizon disappear hull-first.
Travelers going south see southern constellations rise higher above the horizon.
The shadow of the earth on the moon during a lunar eclipse is round.

The earth's circumference was estimated c.240 BC by Eratosthenes, who heard about a place in Egypt where the sun was directly overhead at the summer solstice and used geometry to come up with a circumference of 250,000 stades. This estimate astonishes some modern writers, as it is within 2% of the modern value of 40,070 kilometers.

The Earth's shape can be thought of in two ways;

as the shape of the geoid, the mean sea level of the world ocean, or
as the shape of the Earth's land surface as it rises above and falls below the sea.

As the science of geodesy measured the Earth more accurately, the shape of the geoid was first found not to be a perfect sphere but to approximate an oblate spheroid. More recent measurements have measured the geoid to unprecedented accuracy, revealing mascons beneath the Earth's surface.

In spite of these discoveries, the model of the Earth as a sphere (to a first approximation) remains useful for many purposes. Higher-order features of the Earth's geoid's shape are often represented as spherical harmonics.