Directory of Non-Euclidean Resources

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The study of geometrical systems which differ from that of Eculid, specifically with respect to the 5th or an equivalent to the Parallel Postulate, which states: If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough. This means that in the Euclidean world that lines that are not parallel must inevitably meet. This is not always true in non-Euclidean geometry. This category may also contain webpages with discussion of the validity or otherwise of these different geometries.

Resources in This Category

• Minkowskian Geometry

  http://www.dynamicgeometry.com/General_Resources/Advanced_Sketch_Gallery/Beyond_Euclid/Minkowskian_Geometry.html
  Includes a set of supplementary notes that provide an introduction to Minkowskian geometry and a toolkit for constructing figures.

• Non-Euclidean Geometry

  http://www-groups.dcs.st-andrews.ac.uk/~history/HistTopics/Non-Euclidean_geometry.html
  A historical account with links to biographies of some of the people involved.

• NonEuclid - Hyperbolic Geometry Article & Applet

  http://cs.unm.edu/~joel/NonEuclid/NonEuclid.html
  Software simulation offering straightedge and compass constructions in hyperbolic geometry.

• References for Non-Euclidean Geometry

  http://www-history.mcs.st-andrews.ac.uk/history/HistTopics/References/Non-Euclidean_geometry.html
  A bibliographic reference list of books and articles on non-Euclidean geometries, part of the MacTutor History of Mathematics archive.

• Seminar on the History of Hyperbolic Geometry

  http://www.math.columbia.edu/~pinkham/teaching/seminars/NonEuclidean.html
  Seminar notes by Greg Schreiber.

• Spherical Trigonometry, Arc Distance Formula

  http://www.jqjacobs.net/astro/arc_form.html
  Finding the shortest distance between two points on the earth given latitude and longitude. Download ARC_CALC_3, Microsoft Excel version, A Spherical Triangle Calculator by James Q. Jacobs.

• The Ontology and Cosmology of Non-Euclidean Geometry

  http://www.friesian.com/curved-1.htm
  A philosophical essay.

 

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