Complex Numbers and Geometry
Cambridge 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.
Applications to Geometry
3 The Orthocenter
Angles Subtended by an
B New Year Puzzles
AABC angle angle bisectors becomes C₁ C1 and C2 called centroids circumcircle cocyclic collinear complex numbers complex plane concentric circles condition conjugate consider construct Conversely corresponding defined distance draw equality equation equilateral triangle EXAMPLE expression extensions exterior FIGURE Find fixed points function geometry given gives Hence images interior intersection inversion joining lemma length line segment Mathematical meet midpoint Möbius transformation multiplication nine-point circle Note obtain opposite origin orthogonal pair parallel particular pencil perpendicular positive Proof prove quadrangle radius ratio real numbers relation respectively result roots satisfying Show side BC similar Similarly simply Simson lines solutions Solve square straight lines Suppose symmetric tangent THEOREM transformation that maps unique unit circle vector vertex vertices z-plane