This hands-on workshop will explore the Wurzelschnecke ("root snail"), a simple and elegant spiral construction based on right angle triangles, first attributed to Plato's tutor Theodorus of Cyrene in the 5th C BCE and still studied by mathematicians in our time. We will make and view versions of the Wurzelschnecke at a variety of scales and materials, and play with its possibilities in embodied geometric design in architecture, playground equipment, jewelry, mathematical millinery and more. Our focus will be on its potential use in education, supporting understanding of irrational numbers and trigonometry, and in the geometry of design. I'll share examples from earlier workshops with middle school and high school students, math teachers, grad students and faculty. Workshop participants should have the following materials at hand, if possible: paper, pencil or pen, ruler or straightedge with a square corner, scissors, corrugated cardboard. A protractor and/or carpenter's square are optional but might be helpful.