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