Recent content by belboz

I agree that point uniqueness in the manner you describe is a successful approach to proving that F^-1(C') = C, but I'd consider it an "analytic" vs. "synthetic" solution. It is entirely possible that I am guilty of over-analyzing this particular, simple problem. Perhaps the author expects...

I appreciate your response. At the same time, Modern Geometry with Applications distinguishes RxR (with a distinguished origin and coordinates), from ExE which has neither. In this sense "distance" in ExE appears to be a primitive term, not otherwise defined for the exercise at hand. So...

Clarification (from Jennings): "A function F from ExE to ExE" (he uses E^n for this definition) "is an isometry if for all points p, q in ExE, d(F(p),F(q)) = d(p,q). Let C (in ExE) be the circle with center P and radius r. If F is an isometry from ExE to ExE, prove that F(C) is the...

I just noticed this old thread earlier today, and I would appreciate some clarification on one or two of the points above. A function need only be injective to have an inverse; bijectivity isn't required. Some authors do not define an isometry as a bijection, and state only that it is a...

I agree entirely with the two posts immediately above. Perhaps I should have expanded my original question concerning calculus-based elementary textbooks. The issue more precisely was how best to refresh the knowledge of basic physics (mechanics, E&M) I had at one time, to prepare to deal with...

best -CALCULUS-BASED- text for university physics? I apologize if this question has been addressed in one or another threads, but: given that my basic university physics courses were a very long time ago; and that my elementary, single-variable calculus knowledge seems to have stuck around --...

This text is also used as the basis for MIT's 2006 version of Math 18.01 and 18.02. Please see ocw.mit.edu for details. Wayne