Mathematics is a subject taught from kindergarten through to high school, and yet it is the one subject that most adults are almost proud to admit to not having been very good at, and, therefore, tend to avoid it where they can. However, one of the key factors in mathematics is its ability to enable us to solve everyday problems. When we consider 'the worst-case scenario' of the situation, it is analogous to solving a mathematical problem by considering extremes. Or, we might consider the best path to take from point A to point B, where geometric relationships can be helpful. This book is intended to demonstrate a variety of neglected aspects of mathematics, in order to demonstrate the power and beauty of the field of mathematics beyond where most people, students, and teachers believe is possible.The chapters of the book explore a multitude of topics: unusual arithmetic calculations and shortcuts, entertaining and instructional problem-solving strategies, unusual applications of algebra, and how geometry allows us to better appreciate physical relationships. Only a basic mathematical knowledge is needed to understand these topics and problems; however, the book also demonstrates that, armed with even this level of understanding, our mathematical skills far exceed what we learned at school! The final chapter is the most challenging, and explores a curious problem-solving technique.

Engaging Young Students in Mathematics through Competitions presents a wide range of topics relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment. Following the earlier two volumes, contributors explore a wide variety of fascinating problems of the type often presented at mathematics competitions. In this new third volume, many chapters are directly related to the challenges involved in organizing competitions under Covid-19, including many positive aspects resulting from the transition to online formats. There are also sections devoted to background information on connections between the mathematics of competitions and their organization, as well as the competitions' interplay with research, teaching and more.The various chapters are written by an international group of authors involved in problem development, many of whom were participants of the 9th Congress of the World Federation of National Mathematics Competitions in Bulgaria in 2022. Together, they provide a deep sense of the issues involved in creating such problems for competition mathematics and recreational mathematics.

Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on in school curriculums. The triangle, one of the basic instruments in geometry, has a plethora of unexpected curiosities. Geometric Gems presents one of the largest collections of triangle curiosities currently available, which the authors discuss in an easily understood fashion, requiring nothing more of readers other than the very basics of school geometry to appreciate these curiosities and their justifications or proofs.The book is intended to be widely appreciated by a general audience, and their love for geometry should be greatly enhanced through exploring these many unexpected relationships in geometry. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating triangle properties.

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