21. The set of Euclidean plane isometries forms a composition : the Euclidean group in two dimensions. 22. The familiar Euclidean plane is an affine plane. 23. The case where " X " is the Euclidean plane is the original one of Artin. 24. There are 4 symmetry classes of reflection on the sphere, and two in the Euclidean plane . 25. This corresponds to a point at infinity in the Euclidean plane , no corresponding intersection point exists ). 26. Geometrically, one studies the Euclidean plane ( 2 dimensions ) and Euclidean space ( 3 dimensions ). 27. It is identical to the Euclidean norm, if the complex plane is identified with the Euclidean plane . 28. They also mention that the Euclidean plane version can be proved from the Sylvester-Gallai theorem using induction. 29. For example, if the inclusion space is the Euclidean plane , then the corresponding abstractive classes are lines. 30. Later, Felix Klein realized that Cayley's ideas give rise to a projective model of the non-Euclidean plane .
