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
Skeffington Lutwidge returned to Britain to be refitted and re-coppered in early 1779, after which she returned to North America, capturing the American privateer "Gates" on 29 September 1779. He was involved in the capture of a Spanish convoy on 8 January 1780, and on the night of 16 and 17 January Lutwidge was part of Admiral George Rodney's fleet against Juan de Lángara at the Battle of Cape St. Vincent. His final duties with the "Triton" were to escort a convoy to Menorca and then to the Leeward Islands. Lutwidge then briefly took command of the 74-gun third rate and sailed