The world below is flat. However, there are no endless walls of ice or force or magic - Instead, each side of the octagon "wraps" to the other side.
That is, the North boundary wraps to the South boundary at the exact same point. The North-East to South-West, East to West, and South-East to North-West. There is also a featureless "infinitely" (For all reasonable purposes) tall tower at the cornerpoints, and occupies them all simultaneously.
These wraps function exactly as if you printed this on paper, cut it out, and wrapped one edge to its counterpart. This leads to some... weird navigation around the corners. If you were to walk around the tower, you would walk in three full circles (Measured by angle) before reaching your starting point. Otherwise, navigation is fairly straightforward. Going across the north/south wrap doesn't change your east/west position, etc.
Other information that may be relevant or helpful:
- The planet has two "Suns" - They are always directly across from each other, and rotate around the center of the world.
- The two "Suns" have a "Sun" face and a "Moon" face, which rotate in synch to provide a day/night cycle. Thus, the entirety of the world is at the same time of day. Assume that the day/night cycle functions otherwise like our terrestrial one.
- The central landmass is aproxamately 3600 miles wide by 4600 miles tall. Height of the world is thus aproxamately 10,000 miles. This puts the surface area of the world (And oceans) at around 82.8 million miles squared, a little over 42% of the Earth's surface. (If you want to get into the nitty gritty, each pixel on the map is 5mi per side)
- Gravity is a stable 1g at all points
- The world is truly "flat", and there are no map distortions like you would find on a spherical world.
Religion has imparted the knowledge that the world is the shape it is, and tells of the tower in the corner positions. Even so, some wish to prove that the world is this shape, beyond "blindly" accepting religious dogma.
Using European dating and technology, when would humanity be able to prove this world shape?
Things that are beyond the scope of this question:
- This world affecting technological development. Assume relevant technology and knowledge are exactly what they were historically.
- Magic or other factors that created the world. Assume there is no magic in the world for the purposes of answering this question.
- Changes that the world shape would have on weather, wildlife, geography, etc
- Time needed to prove the world shape. This question is focused solely on technology and knowledge needed to prove it, not how long it would take to accomplish.
A reference for movement across edges: Going North/South across Point 7 takes you to Point 7, North/East from Point 5 takes you to South/West Point 5, etc.
Walking along the coastline, starting at Point 5 heading East, you would go:
- 5 to 4, then cross (West to East)
- 4 to 1, then cross (SE to NW)
- 1 to 2 (Along the "Inner" sea on the top left), then cross back (NW to SE)
- 2 to 6, then cross (SW to NE)
- 6 to 3, then cross (E to W)
- And then you would have a long hike from 3 back to 5 along that very long NW/N coast line.