### A Question of Design

Project of the Month I

Three different design projects are described below, each taken from a real life example. During the first month of class we will be
discussing how (and why) these projects might be adapted for use in your classroom.

**Week 1:** Describe how you would make a pattern for use in one of the projects below. Include an accurate scale drawing of the finished product. Be sure that your technique for constructing the pattern is practical; some angle measures must be given for each polygon, in addition to all edge lengths. If your design requires a circular arc, describe how you would construct that arc in your pattern.

**Week 2:** List the topics that could be taught using the project you chose (e.g. opposite angles are equivalent, the law of cosines, the use of ratios in scale drawings). Sort these topics according to the areas listed in the NCTM Standards document (Number and Operations, Algebra, Geometry, etc.).

**Week 3:** The assignment for week 1 required you to make both design decisions and decisions about the best way to approach the problem. While this is appropriate in a high level college course, it will not work in your average middle school classroom. How would you modify this assignment for use in your own classroom?

**Week 4:** These projects combine topics from geometry, algebra, trigonometry, and art. What class would you use yours in? Would you use it as an end-of-year project, introduce it at the start of the year and return to it periodically, assign it as homework, or complete it during a single class period? Would you be willing to use this in a cross-curricular project with a history, vocational or art class? If so, how would you go about that? If not, why not?

### 1. Pappus' Quilt

Pappus' Theorem states that for a certain arrangement of eight lines,
three particular points of intersection of those lines are always collinear. A few years ago I made a quilt for a friend of mine named Pappas illustrating this theorem.
Design a quilt pattern based on the diagram below.

### 2. Petrie-Coxeter Skew Cube Quilt

By "thinking outside the lines", J.F. Petrie discovered a new way of
creating regular polyhedra. He described two polyhedra to his friend
Donald Coxeter, one of which had six square faces arranged accordian
style around each verex. Each square face was symmetric to each other
face, and each vertex was indistinguishable from every other vertex.
The polyhedron (which Petrie's friend Coxeter dubbed a `honeycomb')
has infinitely many faces and vertices, stretching to infinity in all
directions. This was a surprising new addition to the set of five
platonic solids that have been known since the days of Socrates.
Shown below is a stylized image of six faces of the honeycomb
coming together at a vertex. Design a quilt based on this image.

### 3. Semicircular Window Seat

A bedroom has one semicircular wall with two windows in it. The room
is twelve feet long and is nine feet wide at its narrowest. The
semicircular wall meets the nine foot long walls at an angle of 135
degrees. Design a window seat to fit exactly in the semicircular arc of the wall containing the windows.

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