This book provides an inquiry-based introduction to advanced Euclidean geometry. It utilizes dynamic geometry software, specifically GeoGebra, to explore the statements and proofs of many of the most ...

Euclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. We show that Euclidean geometry can be ...

There is no satisfactory theory of three-dimensional non-Euclidean geometry, from an intuitional point of view, unless it gives us a clear three-dimensional image in our ordinary space, assuming, of ...

THIS book deals only with Euclid's Books III. and IV. Although the original order of the propositions has been maintained, there are many divergences as regards the treatment of his methods. In the ...

This is a preview. Log in through your library . Abstract If X = (X1, ⋯, Xn) has uniform distribution on the sphere or ball in Rn with radius a, then the joint distribution of n1/2a-1 Xi, i = 1, ⋯, k, ...

Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

Geometry may be one of the oldest branches of mathematics, but it’s much more than a theoretical subject. It’s part of our everyday lives, says Professor Jennifer Taback, and key to understanding many ...

I have very fond memories of high school geometry. Memorizing theorems wasn't too hard, and solving proofs was like solving the logic puzzles that I did for fun anyway. But the theorems were scattered ...

Many a mathematician has received a long letter from an unknown sender who claims to have found a way to trisect an angle using only a straightedge and compass. The mathematician may read passages of ...