temarimath.info

Welcome to TemariMath

The site is divided into three sections:

• math studies which use temari as the basis for exploring mathematical ideas. These studies are layered so that you can go into as much detail as you choose.
• pattern investigations which take a particular temari pattern or technique and explore how small changes alter the outcome and create new design possibilities.
• my temari notebook which is the record of all of the temari I make including ones used in the math studies and pattern investigations as well as those that are just for fun (Actually all the temari I make are for fun.)

You can access all of the sections via the contents menu at the right or the sitemap link in the header menu.

So why study temari math?

Curiosity

I'm curious and intrigued by the mathematics inherit in temari designs. Whether you think about it or not when you create one, there is a lot of geometry and arithmetic involved in making a temari. The traditional methods rely upon a paper tape and pins to do all of the measuring and marking but those restrictions do not limit what the artist can create. The symmetry of the designs has always been an important aspect of temari and the established methods make it fairly easy to create very complex and very symmetrical designs without ever worrying about the math. What is it about those methods that allow the artist to create such mathematically complex designs without ever thinking about the spherical geometry involved? How are those methods related to the math and how might they have evolved? For me, understanding some of the underlying mathematics brings a further beauty and grace to the art.

A Greater Understanding of Pattern Structure

This second reason is far more practical. In math it is often useful to group and classify objects in order to more fully understand them, to be sure that something has not been overlooked, and to talk with other people about them using a common vocabulary. I think a similar tactic could be useful with temari designs. What do I mean by that?

Consider triangles as an example. We can classify triangles by the length of their sides (equilateral, isosceles, scalene), or alternately, by their angles (acute, obtuse and right). Notice that in the simple case of triangles, these classifications can overlap, so you could have a right, scalene triangle, that is a triangle with one 90 degree angle and three unequal sides. Understanding the labels used gives you a mental picture of the triangle, and some idea of how to draw it. It can also help you to understand the structure of the item and what the posibilities are for it. (You mean I can't draw an obtuse equilateral triangle?)

I think that considering labels for temari designs can help with understanding the structure and construction of them. It can help us to communicate about them, and maybe it can help us to increase our creativity when we strive to create our own designs. I do not expect there to be an exhaustive scheme, but having any scheme could help with communication and creation. In the temari community we already do this to some extent when we talk about a C8 design or an all-over design. I would like to perhaps expand upon those ideas. Ultimately I hope to apply any classifications I come up with to the notebook pages allowing for sorts and detailed studies of particular types of designs.

New Temari Designs

I see the math as another tool I can use to discover new designs. Just as MC Escher found a need to study symmetry in order to expand his ideas for his artistic tessellations, I see a need to look at the mathematics on the sphere to expand my ideas for temari designs. If I study what the mathematical possibilities are I can broaden my view of just what might be possible on a temari and perhaps take it all a step further when creating my own designs.