Paula Krieg

Hebron, New York, USA

As an artist who makes books and is drawn to math, I have been exploring how the beauty of the paper folding I use to create books is enhanced by mathematical ornamentation. I've been particularly captivated by the structure of the Zhen Xian Bao, also known as Chinese Thread Book, which are folders of layered, flattened, expandable boxes. The many variations of this folkart are based on an understanding the relationship between the sides of a square,and the √2. The varieties of symmetries of these boxes and of their arrangement has led me into looking at the visuals of trigonometric functions. Tethering the boxes to the functions pushes my understanding both of form and of mathematics in a way that is joyfully satisfying.

Chinese Thread Book, Derivative
12 x 31 x 28 cm
Digital Print on Johannot Paper, Book Cloth

Chinese Thread Books don't appear to have a true form, Instead they exist like a family of forms derived from ever changing arrangement based on an understanding of squares and double squares.Consistent with this spirit of variations I've derived a unique configuration of boxes to make a thread book, then decorated them using families of trig functions. To build on the idea of derivative forms, I've overlaid the curves of these functions with their derivatives which compliment the folds and arrangements of the elements of this piece. Furthering the nod to derivatives, one of the patterns used is derived from the primary pattern to create something new.

Function, Derivative, Inverses
30 x 30 cm
Digital Print on Johannot Paper

This print shows one of the papers that was used to make my Chinese Thread Book, Derivative piece. It shows the curves,derivative and inverses of the function (3a/√2)(-sin.3x)^3(cos.5x) between the interval [-pi, pi] with areas between the curves filled with shading and graphics using Adobe Illustrator .My fascination with the art of making appropriate and beautiful graphics to use for my thread books pushes me to develop my graphing skills (thank you, Desmos), my Illustrator skills, and challenges my paper folding and design skills. My attention to both aesthetics and math have to exist and be pushed completely symbiotically when creating this sort of design.