Christopher Bartlett

Professor Emeritus of Art
Towson University
Baltimore, Maryland, USA

Bartlett’s meta-golden Chi ratio is a unique mathematical constant related to the golden ratio.

The Chi (χ) ratio, a solution of Χ²-Χ/ϕ =1, or 1+√(4phi+5)/(2phi) with a value of approximately 1.35567... is a pleasing mathematical number with remarkable generative geometric properties just as the golden ratio (φ). However, instead of partitioning into a square and a φ rectangle, the Chi rectangle of width 1 and a length of Chi, sub-divides into a φ rectangle and another smaller χ rectangle.

More information may be found in Dirk Huylebrouck’s paper, “The Meta-golden Ratio Chi”, Bridges, Seoul, 2014 and our co-authored “Art and Math of the Chi Rectangle”, Symmetry: Culture and Science, 2013.

Cornwall Chi
Cornwall Chi
54 x 40 cm
Acrylic on canvas

The Chi ratio proportion of this canvas generates the interior grid composed by using successive geometric divisions of phi and chi rectangles and squares demarked by visually prominent verticals and horizontals. The composition thus achieves an aesthetically harmonious coherence geometrically correlated to marshal all the various elements into a unified design.