Flatland

I just finished reading 'Flatland: a romance of many dimensions' and I really enjoyed it although having romance in the title is incredibly misleading! It is even more brilliant when you consider it was written in the 19th century and displays such imagination. I'll confess that it took a couple of chapters to get used the style and really immerse myself in the world but after that it was brilliant. I can see why on the back of the book they struggled to categorise the book as either mathematical of scientific as it really has implications for both. I thought I understood the book and then in the next chapter the hexagonal grandson in the 2 dimensional world asked why 3 to the power of 3 didn't work in geometry, its such a simply thought and yet one that had never occurred to me, what are the mathematical implications of 3 to the 4...