For hypothetical beings living in a the surface of a sphere, it is possible to determine if their world is Euclidean or curved and closed by making triangles and measuring the sum of the angles (alternative measure the circumference of circles). For a large sphere they could maybe not notice it at first, but by making the triangle larger and larger they would eventually determine that they are not in an Euclidian space (without the necessity of going to the end of the universe to check).
The same idea of drawing 2d shapes to determine the shape of the universe to works in higher dimensions.
However for beings embedded in a 1+1D line it is not totally clear if there is a way to know if the universe loops back on itself.
Is there a way to determine if the universe is finite in a 1D world without the need to walk or send a signal that loops-back on the whole universe?