欧氏序域上双曲平面的代数构造
An Algebraic Construction of Hyperbolic Planes over a Euclidean Ordered Field
摘要：
利用双线性代数的概念和技巧，构造了欧氏序域上的双曲平面，它满足基本平面几何的所有Hilbert关联、序和同余公理，但对它，双曲形式的平行公理成立，而不是经典的欧氏平行公设成立.
英文摘要：
Using concepts and techniques of bilinear algebra, we construct hyperbolic planes over a euclidean ordered field that satisfy all the Hilbert axioms of incidence, order and congruence for a basic plane geometry, but for which the hyperbolic version of the parallel axiom holds rather than the classical Euclidean parallel postulate.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
