# Christopher Bartlett

Professor Emeritus

Art Department,Towson University

Baltimore, Maryland, USA

Bartlett's Chi Ratio is a mathematical constant related to the golden ratio. He called it the chi ratio as chi (χ) follows phi (φ), the symbol for the golden ratio, in the Greek alphabet.

This meta-golden ratio chi is a pleasing mathematical number with remarkable geometric properties similar to the golden ratio. But instead of partitioning into a phi rectangle and a square, as in the golden ratio, its rectangle sub-divides into phi and chi rectangles.

The chi ratio is one of the solutions of Χ² - Χ/ϕ = 1 and corresponds to [1+√(4ϕ² + 1)]/(2ϕ); its numerical value is 1.355...

This meta-golden ratio chi is a pleasing mathematical number with remarkable geometric properties similar to the golden ratio. But instead of partitioning into a phi rectangle and a square, as in the golden ratio, its rectangle sub-divides into phi and chi rectangles.

The chi ratio is one of the solutions of Χ² - Χ/ϕ = 1 and corresponds to [1+√(4ϕ² + 1)]/(2ϕ); its numerical value is 1.355...

Greek Reflections

40 x 54 cm

acrylic on canvas

2017

Starting with chi ratio canvas dimensions, Bartlett’s composition achieves a reciprocal correlation between the canvas rectangle and the proportional divisions of chi and phi ratio rectangles and squares that structure the interior grid design.

The elements of the painting are aligned with these self-similar areas and consequently at repeating measures from each other. This geometrical underpinning provides the desired aesthetic coherence that marshals all the parts into a unified organizational plan.

The elements of the painting are aligned with these self-similar areas and consequently at repeating measures from each other. This geometrical underpinning provides the desired aesthetic coherence that marshals all the parts into a unified organizational plan.