What are the three methods used by Flatlanders to recognize the shapes of other beings. Define each.
Art of Hearing - Classes are distinguished by hearing another's voice which they can discriminate by class and the friend's own personal voice.
Art of Feeling - Feeling is used by the lower classes ( lower polygons and triangles) and women (lines) in which they feel another's angles.This can be dangerous so the narrator tells us that it is important for the Feeler that the Felt stand perfectly still.
Art of Sight Recognition - This is used by the upper classes where they determine another object's depth. The polygons with sharp angles will fade away with distance more quickly than polygons with broader angles. From what I can tell by the description in the book, the triangle (Merchant) and pentagon (Physician) will appear to a lower class the same: a bright spot at A (the top angle of both) and dimming to D and E. But the upper classes, Aristocracy, can see the difference because they see the light fading more quickly into the fog with the triangle. From the picture, it looks like that is because the angle (A) of the triangle is smaller, thinner and the angle (A) of the pentagon is wider so it simply has more light. The narrator says he might have to ask his friends to rotate if they approach him with their side. He must see them angle first.
The Flatlanders cannot see the sphere. The sphere, being 3-D can be right next to a flatlander without him/her knowing it.
There is a link to the most recent movie and another to a scene from What the Bleep do We Know that depicts a Flatland type of character moving to 3 dimensions.