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 ...

In this note, we obtain the surjectivity of smooth maps into Euclidean spaces under mild conditions. As an application, we give a new proof of the fundamental theorem of algebra. We also observe that ...