This is the hierarchy of shapes, from the lowest respected to the highest:

Click on the name to view a picture of that creature.

 

The Women are the lowest ranking inhabitants of Flatland. They are straight lines, and deadly if you were to run into one of her ends (which are only points). That's why it is the law for women in Flatland to always be making some kind of noise--otherwise she is inwisible unless you look at her broadside.

 

The Soldiers are only slightly more respected than the women. They are isosceles triangles with small vertex angles, and are often rather stupid (because, the bigger the vertex angle, the more intelligence).

 

The Equilateral Triangles are more respected than any woman or isosceles triangle. They say that, with each generation, if everything goes right, that the vertex angle goes up by 1/2 of a degree. So eventually, over time, an isosceles triangle can grow into an equilateral triangle--the first of the regulars.

 

The Square is the kind of creature that the main character (A. Square) is.

 

The Pentagon is a little bit more highly respected--you get the idea: as the amount of sides (of the regular figure) goes up, so does the amount of respect due that person. The general rule here is that one side is added per generation--for instance: A. Square's parents were most likely equilateral triangles, while his children are pentagons (5-sided) and his grandchildren are hexagons (6-sided).

 

After a while, when the number of sides of a person gets to around 400-500, they are (out of respect) called a Circle. The circles are the most highly respected people in all of Flatland and are the rulers of Flatland as well.