A web-based resource for automatic discovery in plane geometry

This column will publish short (from just a few paragraphs to ten or so pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain-teasers involving the use of computers or computational theory. Snapshots are subject to peer review. This issue's snapshot presents another blended dynamic geometry environment. This time, the blend is with an automated reasoning environment. The blended environment enables students to construct and explore geometric constructions, and when they have conjectures about the generality of their findings, they can invoke the automated reasoner to find out under what conditions their conjectures hold. The author illustrates the use of this environment to explore various generalizations of the converse of the Pythagoream theorem.