Andrea Palladio's Renaissance villas are amongst the most famous and widely studied examples of domestic architecture ever produced. The majority of past research about Palladio's architecture employed historical, mathematical and computational methods to analyse their complex proportional systems and rules. In contrast, this paper examines three of Palladio's arguments about his villas plans which relate to their spatial properties and topological connections. Specifically, this paper uses a computational method – the justified plan graph (JPG) – to test two arguments about the location and significance of the primary salon on the plan, and a third about the extent to which the rooms in Palladio's plans are, as he claims, flexible enough to contain alternative functions. Using ten of Palladio's piano nobile (main floor) plans from I Quattro Libri Dell'Architettura as cases, this paper develops mathematical data to test three hypotheses framed around Palladio's plans and theories.

安德里亚·帕拉迪奥 (Andrea Palladio) 的文艺复兴时期别墅是有史以来最著名、研究最广泛的国内建筑范例之一。过去关于帕拉迪奥建筑的大部分研究都采用历史、数学和计算方法来分析其复杂的比例系统和规则。相比之下，本文考察了帕拉迪奥关于他的别墅计划的三个论点，这些论点与他们的空间属性和拓扑连接有关。具体而言，本文使用一种计算方法——合理平面图 (JPG)——来检验关于主沙龙在平面上的位置和重要性的两个论点，以及关于帕拉迪奥平面中房间的范围的第三个论点，如他声称，足够灵活以包含替代功能。使用十个帕拉迪奥'（主楼）从I Quattro Libri Dell'Architettura 的计划作为案例，本文开发了数学数据来测试围绕 Palladio 的计划和理论构建的三个假设。