31. Since the open unit disk is homeomorphic to the Euclidean plane , this is again a one-point compactification. 32. The archetypical example is the real projective plane, also known as the "'extended Euclidean plane " '. 33. Any two-dimensional direct motion is either a translation or a rotation; see Euclidean plane isometry for details. 34. It has been mentioned that circles in the Euclidean plane can not be defined by the focus-directrix property. 35. These can be defined more generally as tessellations of the sphere, the Euclidean plane , or the hyperbolic plane. 36. But notice that the flat Euclidean plane is given by taking p ( x, y ) = 0. 37. Working in a Euclidean plane , he made equipollent any pair of line segments of the same length and orientation. 38. One can view the Euclidean plane as the complex plane, that is, as a 2-dimensional space over the reals. 39. In the Euclidean plane , the conic sections appear to be quite different from one another, but share many properties. 40. In the Euclidean plane , their angles would sum to 450? i . e ., a circle and a quarter.
