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 the Navy, and is listed as a lieutenant in 1763, taking command of the purchased cutter in April that year. He remained with her until 1765, serving in the area of Liverpool. Lutwidge, by now a commander, commissioned the bomb vessel in June 1771, and served in the Irish Sea until the "Carcass" was paid off in April 1773. The "Carcass" was then refitted at Sheerness between March and April for a voyage to the Arctic, with Lutwidge retaining command. The expedition, under the overall command of Constantine Phipps, who commanded , sailed from the Nore on 10 June 1773.