Results for non euclidean space translation from Spanish to English

* the diffeomorphism group of euclidean space r"n" consists of two components, consisting of the orientation preserving and orientation reversing diffeomorphisms.
* the diffeomorphism group of euclidean space r"n" consists of two components, consisting of the orientation preserving and orientation reversing diffeomorphisms.

in particular, in euclidean space, these conditions always hold if the random variables (associated with formula_63 ) are all discrete or are all continuous.
in particular, in euclidean space, these conditions always hold if the random variables (associated with formula_76 ) are all discrete or are all continuous.

* jeremy gray (1989) "ideas of space: euclidean, non-euclidean, and relativistic", 2nd edition, clarendon press.
* jeremy gray (1989) "ideas of space: euclidean, non-euclidean, and relativistic", 2nd edition, clarendon press.

los modelos matemáticos de ganchillo aparecieron más adelante en tres libros de texto sobre geometría que escribieron juntos, de los cuales el más popular es “experiencing geometry: euclidean and non-euclidean with history”.
crocheted mathematical models later appeared in three geometry textbooks they wrote together, of which the most popular is "experiencing geometry: euclidean and non-euclidean with history".