On squaring the circle or circling the square

"If a straight line drawn in a plane revolves uniformly any number of times about a fixed extremity until it returns to its original position, and if, at the same time as the line revolves, a point moves uniformly along the straight line beginning at the fixed extremity, the point will describe a spiral in the plane."

Speculating on Archimedes's treatise On Spirals, Sam Renseiw sets out to squaring the circle, unsure if circling the square (55°40′49″N, 12°35′9″E) would do. In the process, a figure, skating with Sonja Henie's grace, appeared tangentially. View the geometrical footage with "circle-squarers" by clicking here or mouse-skate in above (patafilm # 316, 01'52'', 8.2 MB, Quicktime/mov - Flash version for PC at Blip.tv)