Traditionally, squaring the circle has been about bringing the incommensurable work of the gods within the realm of the commensurate by using infinite cosmic principles to regulate the finite world. The American architect Claude Bragdon (1866-1946) squared the circle using his Theosophic architectural theory that was based on a neo-Pythagorean emphasis on Number, which he believed to have contained the secret of the universe. America at the turn of the 20th century was interested in Eastern spirituality at the beginning of an age of scientific relativity when the world and universe were being questioned due to new scientific discoveries based on higher-dimensional mathematical speculations that challenged relationships between humankind and the cosmos. Paralleling this scientific search was the Western conquest of the world on earth, which brought back speculations about the Near and Far East, including translations of their ancient scriptures and encyclopedias of their architecture. The fourth dimension was an imaginary mathematical (re)creation of great interest to Bragdon and common to scientific relativity and Eastern spirituality; two cultural constructs that altered the perception of time and space to affect the American imagination and architectural production. Within this context, Squaring the Circle investigates the relationship of theory to practice by considering Bragdon's architecture as the material manifestation of his Theosophic architectural theory. / Ph. D.