Circle geometry. An elementary introduction (Q2339748)

The textbook contains the most important and interesting knowledges in connection with circles in geometry. The textbook has 11 chapters. The first chapter starts with several definitions and the Thales theorem and gives examples of Gothic traceries. The second chapter deals with the classical theorems and introductory problems of the circle geometry. The topic of Chapter 3 is radical lines and pencils of coaxial circles. Chapter 4 is devoted to the basic definitions and properties of inversions in a circle. An application is presented, namely a mechanical linkage that would turn circular motion into linear motion. Chapter 5 deals with several famous circles (Apollonius's circle, Feuerbach's circle, Malfatti circles, \dots). Chapter 6 is about cyclic quadrilateral, tangential quadrilateral. The butterfly theorem is mentioned, too. The problems in Chapter 7 are connected with the conformal plane. The subject of Chapter 8 is the ten Apollonius problems. The inversive method is used for the construction of circles that are tangent to three objects in a plane, where the object may be a line, a point or a circle. Chapter 9 considers chains of circles. Among others, the Steiner chain, the Pappus chain and Miquel's six circle theorem are discussed. Chapter 10 is devoted to curves of constant width. After the Reuleaux polygons, it deals with the basic theorems for curves of constant width and the supporting lines. By Barbier's theorem, all curves of the same constant width have equal perimeters. Finally, inequalities are given where the circles and Reuleaux triangles are extremal. The problems in Chapter 11 are connected with constructions. The ruler-and-compass costructions can be done with just a compass according to the Mohr-Mascheroni theorem. The Poncelet-Steiner theorem shows that just a ruler is not enough but a ruler and a single circle with its center is sufficient. Napoleon's problem is considered, too. References and an Index close the book. College and university teachers can use this book. But the book can also be used as a supplement of a problem-solving session for classroom discussions.