The Sun's Shadow
The hyperbolas that have been marked on the floor represent the trajectory of the gnomon's shadow throughout the day and for the different seasons. The curve that is closest to the gnomon corresponds to the path traced by the shadow during the summer solstice, that is, when the Sun's position above the horizon is at its highest. This explains why this shadow is the shortest. The longest shadow, by contrast, corresponds to the winter solstice, when the Sun's position is at its lowest.
A gnomon can also be used as a calendar or sundial. The prolongation of each line towards the East and West indicates where the Sun rises and sets over the course of a year. This point on the horizon corresponds to these cardinal points (East and West) at the equinoxes, when night and day are of equal length. The path traced by the gnomon's shadow at equinox is not a hyperbola, but a straight line.