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Calculating with Conics

In: Perspectives on Projective Geometry

Author

Listed:
  • Jürgen Richter-Gebert

    (TU München, Zentrum Mathematik (M10) LS Geometrie)

Abstract

A major part of classical elementary geometry was concerned with the question of which constructions can be carried out with a straightedge and compass. The decisive primitive operations here are connecting two points by a line, drawing a circle with a radius given by two other points, and marking intersections of objects as new points. In our projective framework we do not have circles, but still can consider elementary constructions with the objects we have studied so far (points, lines, and conics). Since we are interested in particular in calculating with geometric objects, we in particular want to know how we can compute the results of geometric primitive operations if the parameters of the involved objects are given.

Suggested Citation

  • Jürgen Richter-Gebert, 2011. "Calculating with Conics," Springer Books, in: Perspectives on Projective Geometry, chapter 11, pages 189-207, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-17286-1_11
    DOI: 10.1007/978-3-642-17286-1_11
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