# Paula Beardell Krieg

Artist/ Itinerant Arts Educator
Salem, New York, USA

As an artist who teaches bookmaking to students of all ages, I have come to realize that the paper-folding and geometric ornamentation of book arts is a joyful way to explore relationship thinking and specific math ideas. I’ve been particularly captivated by the structure of Chinese Thread Books, Zhen Xian Bao,which are folk-art folders of layered, flattened, expandable boxes I was surprised to discover that in its wide variety of forms, all are fundamentally based on the square. The 2D and 3D geometries of these structures interact in ways that are pleasing, playful, rigorously mathematical and surprising reliant on an understanding of √2.
My constructions of Zhen Xian Baos reflect both my mathematical and artistic inquiries.

A Study of Square within a Chinese Thread Book, which contains 19 separate compartment
21 x 48 x 1 cm
Paper,Decorative Paper, Glue, and Bookcloth
2018

This 4-column thread book hides 19 expandable compartments The elegant ways the various layers of these thread books interact with each other intrigues me. Instructions for constructing them have been hard to come by, largely because Zhen Xian Bao have only been recently introduced in the West. When I have found instructions, a basic style is taught, using specific measurements. Its been my quest to generalize the relationships between the boxes, all of which are based on the square, so as to be able to create many variations. In so doing, I've discovered that using precisely scaled Islamic geometric designs on the papers enables me and my students to better see the relationships we need in order to create our own versions of Zhen Xian Bao.

Chinese Thread Book, a study in orange and gray squares
19 x 22 x 1 cm
Paper, decorative paper, glue and leather
2018

This orange and gray example consists of five layers for a total 14 flattened compartments, each of which expands into a box. These boxes have the footprint of a square or a double square. The bottommost layer is the only exception: It needs to be stretched beyond a true square to accommodate the thickness of the boxes when the whole folder closes. There are six different sizes of boxes here,only four of which can be seen from this angle.This particular folder combines disparate elements of traditional thread books in a way that show various proportional relationships. I use a fourfold Islamic pattern on these papers to help guide folding, making this model a good teaching tool as well as a beautiful object..