This month's reading is the second half of Chapter 2 of Stillwell, starting from section 2.6. The reading is relatively short so this is a good opportunity to review and consolidate what we've done so far, or to catch up if you've fallen behind or joined us late (in which case, welcome!).
Section 2.6 finally delivers the proof of Thales' Theorem that we've waited so long for using the techniques developed earlier in the chapter. The exercises in section 2.8 point towards a profound connection between ruler-and-compass construction and arithmetic that we've been catching glimpses of all along, building on a technique developed in 2.7.
The optional discussion section (2.9) indicates some of the implications of all this, but Stillwell is ready to move on; this month sees us finishing the first of Stillwell's four "pillars", the one relating to axiomatic geometry, and preparing to move out of the ancient world and into the Renaissance.
The book can be purchased here (Amazon link). If you'd like to preview it first, we found an electronic copy hosted here (you need to register). The Moodle site, which has additional resources etc, is here: "enrol" on the course Shape Up using the key COXETER.