This book is about Square, a mathematician who lives in two-dimensional Flatland. He is a very lawful citizen, and goes out of his way to explain to his grandchildren that there is no third dimension, even theoretically. But when he is visited by a sphere from Spaceland, he finds it hard to deny the reality of a third dimension. He is given further reason to consider this possibility when he is granted the rare chance to visit Lineland. He is baffled when the king and queen of that country refuse to acknowledge his existance, because they cannot, in their sphere of experience, imagine that there could be any dimension higher than the first. He is finally convinced when the Sphere allows him to visit Spaceland, where he is able to experience first-hand the third dimension - something he never thought was possible when he lived in Flatland. He then tries his best to convince the rest of the two-dimensional shapes that there's a third dimension, even though they can't see or imagine it.
This report prepared by Phoenix Rye