English

Unsolved And Unsolvable Problems In Geometry

We shall discuss some famous problems which occupied the attention of mathematicians for thousands of years and which have been shown to be unsolvable in recent decades and, in addition, some very old classical problems which, up till now, have scarcely been mentioned in books on the subject. We have endeavoured to vary well-known methods of proof for classical problems and to generalise their formulation. Thus, the object of this book is not the systematic representation of a well-defined section of geometry. But rather our aim is of a methodological nature: we want to develop the kind of arguments which are suitable for the solution of the geometrical problems considered and to discuss the questions implied by the existence of unsolvable problems. In the experience of mathematical institutes and authors of mathematical publications attempts are still made to solve problems which are known to be unsolvable. And so we fear that there will be some readers who, after reading this book, will believe that, despite everything, they have found a solution to the problem of trisecting an angle. We should like to advise these readers as follows: Read through the proof showing that such a so

Sign in with your free account to read, download EPUBs or listen.