Projective Geometry

  • John Stillwell
Part of the Undergraduate Texts in Mathematics book series (UTM)


Perspective may be simply described as the realistic representation of spatial scenes on a plane. This of course has been a concern of painters since ancient times, and some Roman artists seem to have achieved correct perspective by the first century BCE; an impressive example is shown in Wright (1983), p. 38. However, this may have been a stroke of individual genius rather than the success of a theory, because the vast majority of ancient paintings show incorrect perspective. If indeed there was a classical theory of perspective, it was well and truly lost during the Dark Ages. Medieval artists made some charming attempts at perspective but always got it wrong, and errors persisted well into the fifteenth century. [Errors still survive in twentieth-century mathematics texts. Figure 8.1 shows a fifteenth-century artistic example from Wright (1983), p. 41, alongside a twentieth-century mathematical example from the exposé of Grünbaum (1985).]


Projective Geometry Projective Line Conic Section Perspective View Projective View 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsUniversity of San FranciscoSan FranciscoUSA

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