SMARANDACHE NON-GEOMETRY
                                  
                                by         
                            
        Sandy P. Chimienti                       Mihaly Bencze     
        Mathematics and Science Department       6, Hatmanului Street
        University of New Mexico                 2212 Sacele 3
        Gallup, NM  87301, USA                   Jud. Brasov, Romania


Abstract:
  All Euclid's five postulates are denied in this new geometry.

Key Words: Euclidean Geometry, Non-Euclidean Geometry, Smarandache 
           Geometries, Geometrical Model

Introduction:
  We introduce this curious geometry, created in 1969 by F.Smarandache[4], 
and ask for the readers' feedback in finding a model to satisfy the below 
"axioms".

    1. It is not always possible to draw a line from an arbitrary point
       to another arbitrary point.
    
    2. It is not always possible to extend by continuity a finite line
       to an infinite line.

    3. It is not always possible to draw a circle from an arbitrary
       point and of an arbitrary interval.

    4. Not all the right angles are congruent.

    5. If a line, cutting two other lines, forms the interior angles of
       the same side of it strictly less than two right angles,
       then not always the two lines extended towards infinite cut each
       other in the side where the angles are strictly less than two right 
       angles.


Conclusion:
  We thought at a discontinous space to satisfy the first three axioms,
but didn't find yet a corresponding definition for the "right angle".


References:
  [1] Ashbacher, Charles, "Smarandache Geometries", <Smarandache Notions
      Journal>, Vol. 8, No. 1-2-3, Fall 1997, pp. 212-215.
  [3] Chimienti, Sandy P., Bencze, Mihaly, "Smarandache Non-Geometry",
      <Bulletin of Pure and Applied Sciences>, Delhi, India, Vol. 17E,
      No. 1, 115-116, 1998.
  [4] Chimienti, Sandy P., Bencze, Mihaly, "Smarandache Non-Geometry",
      <Smarandache Notions Journal>, Vol. 9, No. 1-2, 45-46, 1998.
  [5] Popov, M. R., "The Smarandache Non-Geometry", <Abstracts of Papers
      Presented to the American Mathematical Society Meetings>, Vol. 17,
      No. 3, Issue 105, 1996, p. 595.
  [6] Smarandache, Florentin, "Collected Papers" (Vol. II), University of
      Kishinev Press, Kishinev, pp. 5-28, 1997.
  [7] Smarandache, Florentin, "Paradoxist Mathematics" (lecture), 
      Bloomsburg University, Mathematics Department, PA, USA, 
      November 1985.