Going straight is represented by following an ellipse on the great section and the movement from one hemiglome to another is represented by the contact between the ellipse and the circumference of the great section.
For every direction at any point in a glome, there is a plane containing the point, the direction and the origin. By cutting the glome with the plane we get a great section mentioned above. So in any direction at any point in a glome we go straight and get to the starting point. This means that a glome can be a representation of a three-dimensional looped space. But the glome shows just the relationship between points, not the shape of the space. The shape of a three-dimensional space is a space.
The distance, area and volume in a glome is different from those in Euclidean geometry. |