Robert Geretschlager

Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The circle, one of the basic aspects of geometry, has a plethora of unexpected curiosities, which the authors present in an easily understandable fashion requiring nothing more 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 readership, whose love for geometry should be greatly enhanced through exploring these many unexpected relationships. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating circle properties.

Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The circle, one of the basic aspects of geometry, has a plethora of unexpected curiosities, which the authors present in an easily understandable fashion requiring nothing more 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 readership, whose love for geometry should be greatly enhanced through exploring these many unexpected relationships. Geometric Gems is also suitable for mathematics teachers, to enhance the education of their students with these highly motivating circle properties.

Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The quadrilateral, one of the basic instruments in geometry, has a plethora of unexpected curiosities. The authors present these in an easily understood fashion, requiring nothing more 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 quadrilateral properties.

Our physical world is embedded in a geometric environment. Plane geometry has many amazing wonders beyond those that are briefly touched on at school. The quadrilateral, one of the basic instruments in geometry, has a plethora of unexpected curiosities. The authors present these in an easily understood fashion, requiring nothing more 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 quadrilateral properties.

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.

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.

The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics — from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses — this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives. The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.

The book presents a comprehensive overview of various aspects of three-dimensional geometry that can be experienced on a daily basis. By covering the wide range of topics — from the psychology of spatial perception to the principles of 3D modelling and printing, from the invention of perspective by Renaissance artists to the art of Origami, from polyhedral shapes to the theory of knots, from patterns in space to the problem of optimal packing, and from the problems of cartography to the geometry of solar and lunar eclipses — this book provides deep insight into phenomena related to the geometry of space and exposes incredible nuances that can enrich our lives. The book is aimed at the general readership and provides more than 420 color illustrations that support the explanations and replace formal mathematical arguments with clear graphical representations.

This book is composed of the most interesting problems from a quarter century of regional mathematics competitions for students aged 11-14 in the province of Styria, Austria. The problems presented here range from pure puzzles to a more traditional mathematical type of question, but all are somehow special, posed with the intent of giving the reader something interesting to think about, with the promise of an entertaining moment of elucidation and enlightenment at the end.

This book is composed of the most interesting problems from a quarter century of regional mathematics competitions for students aged 11-14 in the province of Styria, Austria. The problems presented here range from pure puzzles to a more traditional mathematical type of question, but all are somehow special, posed with the intent of giving the reader something interesting to think about, with the promise of an entertaining moment of elucidation and enlightenment at the end.

This book contains the most interesting problems from the first 24 years of the 'Mathematical Duel', an annual international mathematics competition between the students of four schools: the Gymnázium Mikuláše Koperníka in Bílovec, Czech Republic, the Akademicki Zespól Szkól Ogólnoksztalcacych in Chorzów, Poland, the Bundesrealgymnasium Kepler in Graz, Austria and the Gymnázium Jakuba Škody in Prerov, Czech Republic. The problems are presented by topic, grouped under the headings Geometry, Combinatorics, Number Theory and Algebra, which is typical for olympiad-style competitions. Above all, it is of interest to students preparing for mathematics competitions as well as teachers looking for material to prepare their students, as well as mathematically interested enthusiasts from all walks of life looking for an intellectual challenge.

This book contains the most interesting problems from the first 24 years of the 'Mathematical Duel', an annual international mathematics competition between the students of four schools: the Gymnázium Mikuláše Koperníka in Bílovec, Czech Republic, the Akademicki Zespól Szkól Ogólnoksztalcacych in Chorzów, Poland, the Bundesrealgymnasium Kepler in Graz, Austria and the Gymnázium Jakuba Škody in Prerov, Czech Republic. The problems are presented by topic, grouped under the headings Geometry, Combinatorics, Number Theory and Algebra, which is typical for olympiad-style competitions. Above all, it is of interest to students preparing for mathematics competitions as well as teachers looking for material to prepare their students, as well as mathematically interested enthusiasts from all walks of life looking for an intellectual challenge.

Wouldn't it be great if all school teachers (from kindergarten through high school) would share the joy of mathematics with their students, rather than focus only on the prescribed curriculum that will subsequently be tested? This book reveals some of the wonders of mathematics that are often missing from classrooms. Here's your chance to catch up with the math gems you may have missed. Using jargon-free language and many illustrations, the authors--all veteran math educators--explore five areas--arithmetic, algebra, geometry, probability, and the ways in which mathematics can reinforce common sense. Among other things, you'll learn "the rule of 72," which enables you to quickly determine how long it will take your bank account to double its value at a specific interest rate. Other handy techniques include an automatic algorithm for multiplying numbers mentally and a clever application that will allow you to convert from miles to kilometers (or the reverse) mentally. A delightful presentation of geometric novelties reveals relationships that could have made your study of geometry more fun and enlightening. In the area of probability there is a host of interesting examples: from the famous Monty-Hall problem to the counterintuitive probability of two people having the same birthday in a crowded room. Finally, the authors demonstrate how math will make you a better thinker by improving your organizing abilities and providing useful and surprising solutions to common mathematics problems. You'll come away with an appreciation for math you never thought possible and a true appreciation for this "queen of the sciences."

The circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson's terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements. The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry--leading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves - many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle's place on the sphere bring "full circle" this presentation of a key element of geometry.