A book for secondary school and university teachers that presents various techniques for proving mathematical results in three-dimensional Euclidean space.

A Cornucopia of Quadrilaterals collects and organizes hundreds of beautiful and surprising results about four-sided figures--for example, that the midpoints of the sides of any quadrilateral are the vertices of a parallelogram, or that in a convex quadrilateral (not a parallelogram) the line through the midpoints of the diagonals (the Newton line) is equidistant from opposite vertices, or that, if your quadrilateral has an inscribed circle, its center lies on the Newton line. There are results dating back to Euclid: the side-lengths of a pentagon, a hexagon, and a decagon inscribed in a...

The authors present twenty icons of mathematics, that is, geometrical shapes such as the right triangle, the Venn diagram, and the yang and yin symbol and explore mathematical results associated with them. As with their previous books (Charming Proofs, When Less is More, Math Made Visual) proofs are visual whenever possible. The results require no more than high-school mathematics to appreciate and many of them will be new even to experienced readers. Besides theorems and proofs, the book contains many illustrations and it gives connections of the icons to the world outside of mathematics....

A Panoply of Polygons presents and organizes hundreds of beautiful, surprising and intriguing results about polygons with more than four sides. (A Cornucopia of Quadrilaterals, a previous volume by the same authors, thoroughly explored the properties of four-sided polygons.) This panoply consists of eight chapters, one dedicated to polygonal basics, the next ones dedicated to pentagons, hexagons, heptagons, octagons and many-sided polygons. Then miscellaneous classes of polygons are explored (e.g., lattice, rectilinear, zonogons, cyclic, tangential) and the final chapter presents polygonal...