Scientific method mnemonic: On quest [for] hippos, exercise caution.
Observe: The earth appears flat as I look around in all directions. When the earth is between the sun and moon, it casts a round shadow on the moon. This seems to be true regardless of where one is located on the earth.
Question: What is the shape of the earth?
Hypothesize: I hypothesize that the earth is circular or perhaps a sphere.
Experiment: I find a cubic object, a spherical object, and a conical object. I hold all three objects between a sphere (that represents the moon) and a light source (the sun). I find that the sphere casts a circular shadow on the moon no matter how I hold it. The cone casts a circular shadow in some positions. The cube never casts a circular shadow.
Conclude: Earth appears to be a circle, a cone, or a sphere.