Graham Hancock on archaeology: what the evidence says · JRE #1284
“At a place called Jakosar in the Amazon, you can find a square perfectly enclosing a circle. Now, that is an exercise called squaring the circle that our academics have given to the Greeks. They said the Greeks were the first people who performed that exercise. But now we find in dated sites in the Amazon that this was being done in the Amazon long before the Greeks.”
What the evidence says
Archaeologists have documented hundreds of geometric earthworks, ditched and walled enclosures including squares, circles, and hexagons, some in combined or nested forms, across western Amazonia (Acre, Rondônia, Amazonas states in Brazil, and northern Bolivia), built by pre-Columbian peoples between roughly 1200 BCE and the seventeenth century CE. These sites do predate the era in which Greek mathematicians (5th century BCE onward) formulated "squaring the circle" as a specific problem. However, "squaring the circle" in the historical and mathematical sense refers to a precise geometric construction task, using only a compass and straightedge to build a square with exactly the same area as a given circle, which the Greeks posed as one of antiquity's great unsolved problems and which was later proven mathematically impossible in 1882 once pi was shown to be a transcendental number. An earthwork that places a square shape adjacent to or around a circular shape is a decorative or ceremonial layout choice, not a demonstration of, or solution to, that formal equal-area construction problem. No archaeological or mathematical literature describes the Amazonian earthworks as encoding or solving the Greek quadrature problem; the resemblance is in outward geometric form, not in shared mathematical content or intent.