Final answer:
Without additional context, it's unclear what 'Hexagon' refers to. The provided passages touch on Euclidean and non-Euclidean geometry in relation to the Earth's curvature and artistic perspectives which impacts the angles and sides of triangles.
Step-by-step explanation:
The question seems to reference a conceptual understanding of the geometry of triangles in relation to one's perception, possibly linked to artistic work exploring geometrical perspectives. However, it's not clear what 'Hexagon' is in the context provided. The passages included reference different historical and artistic contexts where geometry plays a role. For instance Eratosthenes' measurement of Earth's circumference involves understanding that the angles observed in Syene and Alexandria imply a curvature to the Earth's surface. Furthermore the description provided about Eliasson's exhibit relates to non-Euclidean geometry, which is a study of geometry on curved surfaces where the sum of the angles of a triangle may not add up to 180 degrees—as would be the case on a plane in Euclidean geometry. In Euclidean geometry, triangles have straight sides and the sum of their internal angles is always 180 degrees.
If the sides were perceived as curved, this would indicate a non-Euclidean space, such as a spherical surface, where triangles can have angles summing to more than 180 degrees. However, without additional context, it's impossible to provide a definitive answer to the original question, "Which direction did Hexagon believe that the sides of the triangle were curved."