Hans Walser Livres

The 99 points of intersection presented here were collected during a year-long search for surprising concurrence of lines. For each example we find compelling evidence for the sometimes startling fact that in a geometric figure three straight lines, or sometimes circles, pass through one and the same point. Of course, we are familiar with some examples of this from basic elementary geometry - the intersection of medians, altitudes, angle bisectors, and perpendicular bisectors of sides of a triangle. Here there are many more examples - some for figures other than triangles, some where even more than three straight lines pass through a common point. The main part of the book presents 99 points of intersection purely visually, developed in a sequence of figures. In addition the book contains general thoughts on and examples of the points of intersection, as well as some typical methods of proving their existence.

The Golden Section has played a part since antiquity in many parts of geometry, architecture, music, art and philosophy. However, it also appears in the newer domains of technology and fractals. This book aims both to describe examples of the Golden Section, and to show some paths to further developments.

Mathematical patterns and regularities of spirals and helixes are explored through visually appealing geometric representations and analytical insights. The book covers various types of spirals, including round, square, golden, and spherical, highlighting their curvature behavior and unique properties using examples from technology and nature. With a modular structure, each chapter can be read independently, making it a valuable resource for students, teachers, and anyone interested in mathematics.

Focusing on the Golden Ratio, this book explores its significant mathematical properties, particularly in geometry and number theory. It presents various connections and examples, enhancing understanding through accessible explanations and generalizations, making complex concepts approachable for readers interested in mathematics.

An examination of symmetry for the interested layman.

Mathematische Muster und Regelmäßigkeiten von Spiralen und schraubenförmigen Figuren stehen im Mittelpunkt dieses Buches. Es bietet eine visuell ansprechende und analytische Aufbereitung geometrischer Aspekte und untersucht verschiedene Spiralen, darunter runde, eckige und goldene. Anhand von Beispielen aus Technik und Natur werden deren Krümmungsverhalten und weitere Eigenschaften beleuchtet. Der modulare Aufbau ermöglicht ein unabhängiges Lesen der Kapitel, was das Buch zu einer wertvollen Ressource für Studierende, Lehrkräfte und mathematisch Interessierte macht.

Leben auf der Kugel. Verzerrungen. Kartenträger.Abstandstreue Entwürfe. Gnomonische Projektion.Flächentreue und winkeltreue Karten. Quer und schief.Von der Plattkarte zur Herzkarte. Sphärische Vielecke.Sphärische Trigonometrie.Literatur und Websites. Namen- und Sachverzeichnis.