Education Technology

Spirally Surds

Activity Overview

Students start by constructing the Spiral of Theodorus by hand using traditional pen and paper techniques. Once they have the general construction idea, they produce the spiral using the dynamic geometry facilities of TI-Nspire. The length of the hypotenuse is then explored as the spiral progresses. 


The purpose of this activity is to engage students in the lovely visual representation (Spiral of Theodorus) and see how it provides a natural progression of a series of surds. 


  • Surd
  • Spiral of Theodorus
  • Perpendicular

About the Lesson

In this activity students use traditional pencil and paper techniques to construct the Spiral of Theodorus, after which they use the Geometry application on TI-Nspire to make the spiral dynamic. Students then explore consecutive hypotenuse, a series of surds, helping connect geometry and number.