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Generalization of Apollonius Theorem In Triangle Geometry: Results in Elementary Mathematics
This book contains some exciting generalization of the above Apollonius theorem. The book is divided into 5 chapters. Each chapter is divided into 4 parts namely
i) Actual statement of theorem
ii) Proof of the theorem.
iii) Application to find length of the remaining line segment when all other lengths are given. ( Exactly 3 examples are discussed. )
iv) All the segment lengths are given and we have to verify whether the given triangle exists or not. ( Exactly 3 examples are discussed. )
Following are the salient features why reader should buy the current book.
-This book contains originality. It means in most chapters things are discussed, which we will not find in any other book. Even if particular concept is found in some book or website, author has represented it in a little different way.
-In each chapter author has given 3 examples of each theorem to find the remaining length once all other lengths are given and 3 examples to check existence of the triangle so that reader will not have any doubt.
-Almost all the chapters are having different style from traditional learning mathematics taught in school or college or in books.
Only pre-requisite to read this book is to know Apollonius theorem for median of a triangle which is given above and in the first chapter along with the examples. Other than that each chapter has been discussed separately. No prior knowledge of any other theorem except Pythagorous theorem for right angled triangle is required.
After reading this book, people who have hatred feeling for geometry especially triangles can develop liking for it.
Methods to calculate various lengths of the triangle can be useful for competitive exam also.
The book contains elementary mathematics knowledge that of school mathematics and level of the book is kept to absolutely elementary.
Examples are explained step by step and are plenty in number and any student above seventh standard can understand it. Also topics range from elementary to challenging level.
Following are the generalization methods of Apollonius theorem discussed in this book
Hence this book can be considered as bible of Apollonius theorem and it’s extension for triangles.
à When several (or one) segments are drawn from vertex of a triangle to base, then length of the remaining segment can be found using Apollonius theorem or it’s generalizations.
à Theory behind every concept is explained which will help keen mathematics students proud. Superficial readers may skip proof of the theorem and read only the applications. Although we suggest that proof will enhance concepts in geometry especially triangle
geometry.
For pure mathematics students and teachers this book will be very helpful for further studies in geometry.
i) Actual statement of theorem
ii) Proof of the theorem.
iii) Application to find length of the remaining line segment when all other lengths are given. ( Exactly 3 examples are discussed. )
iv) All the segment lengths are given and we have to verify whether the given triangle exists or not. ( Exactly 3 examples are discussed. )
Following are the salient features why reader should buy the current book.
-This book contains originality. It means in most chapters things are discussed, which we will not find in any other book. Even if particular concept is found in some book or website, author has represented it in a little different way.
-In each chapter author has given 3 examples of each theorem to find the remaining length once all other lengths are given and 3 examples to check existence of the triangle so that reader will not have any doubt.
-Almost all the chapters are having different style from traditional learning mathematics taught in school or college or in books.
Only pre-requisite to read this book is to know Apollonius theorem for median of a triangle which is given above and in the first chapter along with the examples. Other than that each chapter has been discussed separately. No prior knowledge of any other theorem except Pythagorous theorem for right angled triangle is required.
After reading this book, people who have hatred feeling for geometry especially triangles can develop liking for it.
Methods to calculate various lengths of the triangle can be useful for competitive exam also.
The book contains elementary mathematics knowledge that of school mathematics and level of the book is kept to absolutely elementary.
Examples are explained step by step and are plenty in number and any student above seventh standard can understand it. Also topics range from elementary to challenging level.
Following are the generalization methods of Apollonius theorem discussed in this book
Hence this book can be considered as bible of Apollonius theorem and it’s extension for triangles.
à When several (or one) segments are drawn from vertex of a triangle to base, then length of the remaining segment can be found using Apollonius theorem or it’s generalizations.
à Theory behind every concept is explained which will help keen mathematics students proud. Superficial readers may skip proof of the theorem and read only the applications. Although we suggest that proof will enhance concepts in geometry especially triangle
geometry.
For pure mathematics students and teachers this book will be very helpful for further studies in geometry.
75 pages, Kindle Edition
First published March 22, 2014
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