During an equinox (March 20 and September 22-23), the Sun is directly above the equator. If we are on the equator, an upright stick will not have a shadow in the middle of the day.
On any other location, the angle between the stick and the direction of sunlight will be the same as the observer’s latitude.
This fact can only occur if the Earth is a sphere, and only if the Sun is very far relative to the size of the Earth.
Geometrical diagram:
