Harmonic Perspective

C. J. Fearnley and Jeannie Moberly
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 481–484


In projective geometry basic incidence relations and duality are primary. Perspective is an elementary relation between points or lines linked to perspective drawing. Harmonics are little known but pervasive geometric invariants featuring a fundamental fourness divided into two pairs. We discuss several definitions of harmonics, from ones involving basic incidence constructions to non-projective ones with circles, angles and distance ratios. This preliminary study provides a glimpse into the possibilities of harmonic perspective. We describe three artworks that explore harmonics, perspective and their interrelationships. They are composed on hardboard painted with acrylic and oil.