Notre-Dame in Paris ranks among the world’s most famous buildings, and the broad outlines of its history are well understood.1 Generations of scholars using documentary and archaeological evidence have traced the main stages of the cathedral’s development from the official placement of its cornerstone in 1163 up to the tragic fire that damaged its fabric in 2019.2 Despite this veneer of familiarity, however, Notre-Dame incorporates many subtle features and anomalies that have never been explained adequately, and the overall logic of the cathedral’s design has received surprisingly little systematic attention. The present essay explores how the method of geometrical analysis enables us to better understand these issues.

Fundamentally, this method involves an attempt to see the cathedral as a medieval builder might, asking what sequences of geometrical operations could have generated its forms, first at the drawing board and then at the work site.3 In principle, such...

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