Complex Numbers and GeometryCambridge University Press, 1994 - 192 páginas The purpose of this book is to demonstrate that complex numbers and geometry can be blended together beautifully. This results in easy proofs and natural generalizations of many theorems in plane geometry, such as the Napoleon theorem, the Ptolemy-Euler theorem, the Simson theorem, and the Morley theorem. The book is self-contained - no background in complex numbers is assumed - and can be covered at a leisurely pace in a one-semester course. Many of the chapters can be read independently. Over 100 exercises are included. The book would be suitable as a text for a geometry course, or for a problem solving seminar, or as enrichment for the student who wants to know more. |
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angle bisectors arbitrary points C₁ and C2 Cantor centroids circles C₁ circumcenter circumcircle circumcircle of ABC cocyclic collinear complex numbers complex plane concentric circles conjugate COROLLARY cross ratio equality equilateral triangle EXAMPLE exterior angle FIGURE fixed points four points geometry given Hence imaginary incircle inscribed integers intersection inversion lemma line passing line segment joining Mathematical midpoint Möbius transformation multiplication nine-point circle number system obtain orthocenter orthogonal P3 with respect pair of circles pair of concentric parallel pencil of circles perpendicular bisector point at infinity points 21 Proof radius real axis real numbers Riemann sphere satisfying Show side BC Simson lines solutions square straight lines Suppose tangent THEOREM transformation that maps triangle inequality trisectors unit circle vector vertex vertices w₁ z-plane αβ βγ γα