| 31. | Fixing one such point as a midpoint actually defines an affine structure on the projective line containing that range.
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| 32. | First, one can replace the projective line by an " n "-dimensional projective space.
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| 33. | One of the Italian mathematicians was Giovanni Vailati who studied the circular order property of the real projective line.
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| 34. | The Riemann sphere is one example of a complex algebraic manifold, since it is the complex projective line.
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| 35. | The converse of this observation ( except for the projective line ) is the fundamental theorem of projective geometry.
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| 36. | I don't understand how the cross ratio answers when 4 points in projective line are projectivly equivalent.
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| 37. | Nevanlinna theory addresses the question of the distribution of values of a holomorphic curve in the complex projective line.
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| 38. | Many curves, for example hyperelliptic curves, may be presented abstractly, as ramified covers of the projective line.
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| 39. | Abstractly we can say that this is a projective line in the space of all conics, on which we take
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| 40. | A homography of a projective line may also be properly defined by insisting that the mapping preserves cross-ratios.
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