# Christopher Bartlett

Professor Emeritus of Art

Towson University

Baltimore, Maryland, USA

I am interested in the geometry of composition in painting. I discovered the Meta-Golden Chi ratio while analyzing master paintings. The Meta-Golden Chi (χ) ratio, a solution of x²-x/φ =1, or 1+√(4φ +5)/(2φ) with a value of 1.3556... 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 golden ratio rectangle and another smaller Chi rectangle. My compositions are structured and unified using an underlying meta-golden grid that yields golden ratio divisions, consequent squares, and Chi ratio rectangles.

1.35 x

54 x 40 cm

acrylic on canvas

2018

This imagined scene was an altered and reconstructed reality to create a visually pleasing artwork employing a mathematical composition. Starting with a 1.35 Meta-Golden ratio Chi canvas dimensions, a line drawn from an opposite corner perpendicular to the canvas diagonal becomes the diagonal of a smaller rectangle. That smaller rectangle is in the same proportion as the original Chi canvas rectangle. The remaining rectangle is a Phi rectangle. There are two stacked Phi rectangles separated by the horizontal of the balcony in this painting. The lower edge is delineated by the horizontal of the dockside. Each implied mathematical alignment is governed by the Chi ratio and its divisions.

1.35 y

54 x 40 cm

acrylic on canvas

2018

This work follows a similar Meta-Golden compositional procedure. The bottom edge of the balcony is the base of the Phi rectangle. As in an architect's design, subsequent divisions in the composition achieve an aesthetically harmonious coherence: a structure where the verticals, horizontals, and divisions at edges are mathematically aligned to marshal all the elements into a self -similar unified organizational plan.