Descriptive Topology

  • George K. Francis


Descriptive topology, namesake of descriptive geometry, serves contemporary topology in the same manner as its forbearer served the geometry of the nineteenth century. In the eleventh edition of the Encyclopedia Britannica, Henrici defines descriptive geometry as that branch of the discipline “which is concerned with the methods of representing solids and other figures in three dimensions by drawings in one plane.” The rigor with which this subject used to be taught was justified by its application in the preparation of accurate architectural and engineering drawings. Photography first, and more recently, computer aided design, have greatly reduced the need for its study in our schools. At the same time, the immense expansion of topology in this century, both as a pure and as an applicable science, has produced a sizeable collection of basic examples and a variety of styles for their exposition. “Descriptive topology” is an apt name for their systematic study.


Triple Point Descriptive Geometry Descriptive Topology Picture Plane Pinch Point 
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Copyright information

© Springer Science+Business Media New York 2007

Authors and Affiliations

  • George K. Francis
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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