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", , Vol. 8, No. 1-2-3, Fall 1997, pp. 212-215.
[3] Chimienti, Sandy P., Bencze, Mihaly, "Smarandache Non-Geometry",
, Delhi, India, Vol. 17E,
No. 1, 115-116, 1998.
[4] Chimienti, Sandy P., Bencze, Mihaly, "Smarandache Non-Geometry",
, Vol. 9, No. 1-2, 45-46, 1998.
[5] Popov, M. R., "The Smarandache Non-Geometry", , 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.