From Bolyai's Geometry to Smarandache Anti-Geometry. From: Smarandache Notions Journal | Date: January 1, 2000| Author: Vasiu, Angela; Oprea, Nicolaie | COPYRIGHT 2000 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan.  All inquiries regarding rights should be directed to the Gale Group.Copyright information

ABSTRACT

It is considered the notion of absolute Geometry in its evolution, from the first Non-euclidean Geometry of Lobacewski, Bolyai and Gauss till that of Smarandache Anti-Geometry.

Key words: Euclidean Geometry, Non-euclidean Geometry, Hilbert's axioms and incidence structures deduced from them, Smarandache Geometries, Hjelmslev-Barbilian structures

Any theory or deductive system has two distinguishable parts:

1. the specifical part...