chapter  1
Introduction
Pages 11

Eric Knuth, in his article "Fostering Mathematical Curiosity", makes rich use of the "What-If-Not" problem-posing scheme. He presents two problems that illustrate ways for teachers to engage students in problem posing and in so doing to foster mathematical curiosity. Here the author wishes to focus on his second problem because he gives both a technology-based solution and an analytic solution for it. He explores and then answers that question in the form of a conjecture by using the help of various features of the Geometer's Sketchpad. He then also offers an analytic proof of his conjecture. Marion Walter was being shown how to use the "Geometry Inventor" dynamic geometry program by staff members of the Education Development Center, which included Al Cucuo and Paul Goldenberg. Prior to asking the dynamic geometry program to calculate the ratios, no one present guessed correctly that the constant ratio was, surprisingly.