Geometry is one of the most beautiful aspects of mathematics. This beauty is because you can 'see' geometry at work. Most people are exposed to the very basic elements of geometry throughout their schooling with the most concentrated study in the secondary school curriculum. High schools in the United States offer one year of concentrated study of geometry that shows students how a mathematician functions, since everything that is accepted beyond the basic axioms must be proved. Unfortunately, as the course is only one year long, there is still very much in geometry left unexplored for the general audience. That is the challenge of this book, in which we will present a plethora of amazing geometric relationships.
We begin with the special relationships of the Golden Ratio, before considering unexpected concurrencies and collinearities. Next, we present some surprising results that arise when squares and similar triangles are placed on triangle sides, followed by a discussion of concyclic points and the relationships between circles and various linear figures. Moving on to more advanced aspects of linear geometry, we consider the geometric wonders of polygons. Finally, we address geometric surprises and fallacies, before concluding with a chapter on the useful concept of homothety, which is not included in the American year-long course in geometry.
Contents:
- About the Authors
- Introduction
- The Golden Ratio in Geometry
- Unexpected Concurrencies
- Unexpected Collinearities
- Squares on Triangle Sides
- Similar Triangles on Triangle Sides
- Discovering Concyclic Points
- Circle Wonders
- Polygons and Polygrams
- Geometric Surprises
- Geometric Fallacies
- Homothety, Similarity, and Applications
- Index
Readership: This book is suitable for secondary/high school level students and teachers, as well as a general readership, particularly those interested in bridging the gaps in their knowledge of geometry.
Alfred S Posamentier is currently Distinguished Lecturer at New York City College of Technology of the City University of New York. Previously, he was the Executive Director for Internationalization and Sponsored Programs at Long Island University, New York. This was preceded by a five-year period where he was Dean of the School of Education and tenured Professor of Mathematics Education at Mercy College, New York. He is now also Professor Emeritus of Mathematics Education at The City College of the City University of New York, and former Dean of the School of Education, where he was tenured for 40 years. Hans Humenberger has been a Professor of Mathematics at the University of Vienna, Austria, since 2005. From 2000-2005 he was Associate Professor at the University of Dortmund (Germany). His particular interests lie in teaching mathematics as a process (not a ready product), applications of mathematics and problem solving. Regarding the last topic, he teaches a seminar every year with student teachers at his university. Since 2007 he has been the editor of an Austrian school mathematics textbook series for grades 5–8 and has initiated a program for grade 5–8 students at the university in order to enhance their experience with problem solving. He has edited and written several books in German and has written many contributions in English for several journals.
Geometry is one of the most beautiful aspects of mathematics. This beauty is because you can 'see' geometry at work. Most people are exposed to the very basic elements of geometry throughout their schooling with the most concentrated study in the secondary school curriculum. High schools in the United States offer one year of concentrated study of geometry that shows students how a mathematician functions, since everything that is accepted beyond the basic axioms must be proved. Unfortunately, as the course is only one year long, there is still very much in geometry left unexplored for the general audience. That is the challenge of this book, in which we will present a plethora of amazing geometric relationships.
We begin with the special relationships of the Golden Ratio, before considering unexpected concurrencies and collinearities. Next, we present some surprising results that arise when squares and similar triangles are placed on triangle sides, followed by a discussion of concyclic points and the relationships between circles and various linear figures. Moving on to more advanced aspects of linear geometry, we consider the geometric wonders of polygons. Finally, we address geometric surprises and fallacies, before concluding with a chapter on the useful concept of homothety, which is not included in the American year-long course in geometry.
Contents:
- About the Authors
- Introduction
- The Golden Ratio in Geometry
- Unexpected Concurrencies
- Unexpected Collinearities
- Squares on Triangle Sides
- Similar Triangles on Triangle Sides
- Discovering Concyclic Points
- Circle Wonders
- Polygons and Polygrams
- Geometric Surprises
- Geometric Fallacies
- Homothety, Similarity, and Applications
- Index
Readership: This book is suitable for secondary/high school level students and teachers, as well as a general readership, particularly those interested in bridging the gaps in their knowledge of geometry.
Alfred S Posamentier is currently Distinguished Lecturer at New York City College of Technology of the City University of New York. Previously, he was the Executive Director for Internationalization and Sponsored Programs at Long Island University, New York. This was preceded by a five-year period where he was Dean of the School of Education and tenured Professor of Mathematics Education at Mercy College, New York. He is now also Professor Emeritus of Mathematics Education at The City College of the City University of New York, and former Dean of the School of Education, where he was tenured for 40 years. Hans Humenberger has been a Professor of Mathematics at the University of Vienna, Austria, since 2005. From 2000-2005 he was Associate Professor at the University of Dortmund (Germany). His particular interests lie in teaching mathematics as a process (not a ready product), applications of mathematics and problem solving. Regarding the last topic, he teaches a seminar every year with student teachers at his university. Since 2007 he has been the editor of an Austrian school mathematics textbook series for grades 5–8 and has initiated a program for grade 5–8 students at the university in order to enhance their experience with problem solving. He has edited and written several books in German and has written many contributions in English for several journals.
A JOURNEY THROUGH THE WONDERS OF PLANE GEOMETRY
456
A JOURNEY THROUGH THE WONDERS OF PLANE GEOMETRY
456Related collections and offers
Product Details
| ISBN-13: | 9789811292866 |
|---|---|
| Publisher: | WSPC |
| Publication date: | 01/24/2025 |
| Series: | PROBLEM SOLVING IN MATHEMATICS AND BEYOND , #34 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| Pages: | 456 |
| File size: | 53 MB |
| Note: | This product may take a few minutes to download. |