# Christopher Bartlett

I discovered a unique rectangle while analyzing the compositional geometry of master paintings, in particular painter, Fairfield Porter.

In 2005 I presented this in a paper at Bridges Banff. Recently, my artistic discovery has proven to have mathematical validity with an aspect ratio of 1+√(4phi+5))/(2phi) = 1: 1.355…

This rectangle (I call 'Chi') has generative properties similar to the golden ratio ('Phi') rectangle itself. In 2013, I co-authored a paper with Dirk Huylebrouck, “Art and Math of the Chi Rectangle”.

His paper, “The Meta-golden Ratio Chi” presented at this Seoul 2014 conference explains its mathematical significance in depth.

Starting with Chi ratio canvas dimensions, if a line is drawn from an opposite corner perpendicular to a diagonal, that line is the diagonal of a smaller rectangle that is in the same proportion to the Chi canvas rectangle and the remainder is a Phi rectangle.

It can partition the structure of the painting into successive repetitions of the Chi and Phi proportions, varied but each integrally related to form a visually unified whole. The Chi rectangle presents a more compact shape than the Phi rectangle and is an appealing alternative for design and composition.

In my paintings I have used the Chi proportions of the canvas to structure the interior geometric design where the main horizontal division (or vertical, if in a horizontal canvas) gives a Phi rectangle at the base and a Chi rectangle above. The visually dominant vertical divides that upper Chi rectangle again into another similar rectangle and another Phi rectangle, and so on.

The handrail of the bridge in Grand Canal is composed at the horizontal that defines the upper Chi and lower Phi rectangles, Hydra is divided at the shadow edge of the building and it is the edge of the dock in Fiskardo.

The verticals of Fiskardo's lamp post and the edge of Grand Canal's orange building partitions the upper Chi rectangle into another set of Chi and Phi rectangles. This principal vertical is drawn at the perpendicular from the intersection of the original diagonal and horizontal.