Some mathematical properties of the Bartlett chi ratio

Based on artistic interpretations, art professor Christopher Bartlett (Towson University, USA) suggested introducing a new mathematical constant related to the golden ratio. He called it the chi ratio, as chi follows phi in the Greek alphabet. Without going too much into the artistic considerations, which may be subject to criticism similar to the golden ratio debunking, we focus on showing that the chi ratio is interesting as a number as such, with remarkable geometric properties, just as the golden ratio is.