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
Pen name may use different pen names for each, sometimes with no attempt to conceal a true identity. Romance writer Nora Roberts writes erotic thrillers under the pen name J. D. Robb (such books are titled "Nora Roberts writing as J. D. Robb"); Scots writer Iain Banks wrote mainstream or literary fiction under his own name and published science fiction under Iain M. Banks; Samuel Langhorne Clemens used the aliases Mark Twain and Sieur Louis de Conte for different works. Similarly, an author who writes both fiction and non-fiction (such as the mathematician and fantasy writer Charles Dodgson, who wrote as Lewis