First of all, author wants from us to imagine that a vast paper which has only geometric sahapes. Actually, I thought that is a restriction of our dream world because generally when we thinking about something we imagine like three dimentional, I guess. Also he said that geometric shapes are only two dimentional. According to authors example, I think that when we see something we take photo of it by our eyes and it became a two d. in our mind. maybe it is because of this, I am not sure. Another interesting is that, author categorized the geometric shapes in accordance with number of their line. From what I read, It is different thing that there is an hierachy between the shapes. For example, women are straight line that is the low level of status. I have a question there. Why women are low of this hierachy? Shapes which have higher status can experience each other but others not. Why? Actually, I think that relevant with geometry, hierarchical status are only for attracts readers attention. For example, circle has the highest status, is made also only one continuous line. I am not sure about but I think circle can change itself from 2D to 3D so, it has the highest status. Also same logic, straight line cannot change itself like circle. I do not know what is the logic behind the hierarchical reason but I think that if geometric shapes which are in 2D change himself to 3D, maybe they will wriggle their strict hierarchical societies.
That is part of Flatland what I have read and thougt on it.