# Lewis Carroll Meets the Imaginary Number

### By Thomas K. Simpson & Anne Farrell

Early in his life, long before he met Alice and plunged down that rabbit hole into Wonderland, Lewis Carroll was given a very curious math problem. It was a simple equation, but it had no solutions in the world of real numbers (the counting numbers, with all their fractions and multiples). All its solutions, but zero, were imaginary!

He looked in vain for a way to see them – an imaginary plane perhaps, on which they might be graphed. He couldn’t find one, but we can!

To capture imaginary numbers, we need *four dimensions*. In this book, we enter the world of four dimensions, find the elusive imaginary plane, and with its help, produce the very graph Lewis Carroll was looking for. *It’s our front cover!*