论文标题
双曲机的简单基础
Simple Foundations for the Hyperbolic Plane
论文作者
论文摘要
H. L. Skala（1992）通过替换Menger的公理，涉及Pappus和Desargues的定理，为双曲线平面定理提供了第一个优雅的一阶公理系统，用于双曲线几何。在这样做时，Skala表明双曲线几何形状是发生率的几何形状。我们通过将Pappus和Desargues完全取代，替换两个简单的公理，从而改善了Skala的配方。
H. L. Skala (1992) gave the first elegant first-order axiom system for hyperbolic geometry by replacing Menger's axiom involving projectivities with the theorems of Pappus and Desargues for the hyperbolic plane. In so doing, Skala showed that hyperbolic geometry is incidence geometry. We improve upon Skala's formulation by doing away with Pappus and Desargues altogether, by substituting for them two simpler axioms.
