The researcher Allan Brown had been led on a similar trajectory, his obsession with the circles drawing him into the study of sacred geometry. At the 2003 Glastonbury Conference, Brown presented a talk that was the culmination of his years of research, proposing a solution to a central mystery: The hidden reason for the “quintuplet” patterns – four smaller circles arrayed around one large one – that had been among the earliest formations recorded, first showing up in 1978, and among the most frequent, appearing every year without fail. Over time, Brown realized that these quintuplets were related to the ancient conundrum of the squared circle. Implicit in their relationships, teased out through careful geometric analysis and the drawing of implicit tangent lines, was a series of previously unknown methods for performing this difficult intellectual feat that had obsessed the Classical mind.
“The circle is a symbol of spirit, of heaven, of the unmanifest, the immeasurable and the infinite, while the square is the symbol of the material, the Earth, the measurable and the finite,” Brown said, noting that the symbolic essence of the problem was the reconciliation of seemingly opposing principles, and the resolution of dualities – “a sacred, cosmological act.” Over twenty-five years, the differently proportioned quintuplets functioned as an instruction manual for the squared circle, suggesting dozens of new methods – some within 99.9999 percent accuracy – for solving this dilemma. “They were actually teaching a methodology, a complete system, through which a geometric solution to the squaring of the circle could be attempted.” Brown also proposed that this quarter-century project argued against human hoaxing. “Can so many formations, over so many years, adhere to such a sublime design principle, without anyone ever, in a quarter of a century, coming forward to hint at the geometric properties they were encoding into their designs?”