Non-Euclidean geometry caused a re-examination of the teaching of geometry based on Euclid's Elements. This curriculum issue was hotly debated at the time and was even the subject of a book, "Euclid and his Modern Rivals", written by Charles Lutwidge Dodgson (1832–1898) better known as Lewis Carroll, the author of "Alice in Wonderland". In analytic geometry a plane is described with Cartesian coordinates : "C" = { ("x,y") : "x", "y" ∈ ℝ }. The points are sometimes identified with complex numbers where ε ∈ { –1, 0, 1}. The Euclidean plane corresponds to the case since the modulus of is given
Lewis Carroll his two sons were hardly more than babies. The older of these sons – yet another Charles Dodgson – was Carroll's father. He went to Westminster School and then to Christ Church, Oxford. He reverted to the other family tradition and took holy orders. He was mathematically gifted and won a double first degree, which could have been the prelude to a brilliant academic career. Instead, he married his first cousin Frances Jane Lutwidge in 1830 and became a country parson. Dodgson was born in the small parsonage at Daresbury in Cheshire near the towns of Warrington and Runcorn, the