Since 1997 Tom Apostol and Mamikon Mnatsakanian have co-authored 30 papers, most of which are on geometry. Their work is strikingly innovative, combining the classical with the modern. They often surprise the reader with fresh, frequently astounding conclusions that challenge the imagination. As an added attraction to the reader, only a modest background is needed to understand their work. Working together, they have won three Lester R. Ford Awards since 2005 for five papers published in the American Mathematical Monthly in 2004, 2007, and 2009 — an enviable achievement.

The citation for their 2004 Ford Award notes that they do classical geometry with a modern twist, and modern geometry with a classical twist, obtaining new and surprising results in areas that have been mined for centuries. Their writing is hailed as a model of the succinct and the elegant, and a rich mix of the new and the classical.

This book gathers together several of their papers that constitute a royal road through several parts of classical geometry with spectacular side trips down lanes that previously were not known. In this volume they have expanded on the original papers and added exercises. Their writing also brings new richness to calculus. Newton and Leibniz would likely have been grateful for their wonderfully intuitive insights. Mamikon's approach to many integration problems has great power and should be more widely known.