Hans Walser - Böcker

Translated from the original German by Peter Hilton and Jean Pedersen. 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. They are developed in a sequence of figures, many without caption or verbal commentary. 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. Many of the examples shown in the book were inspired by questions and suggestions made by students and high-school teachers. Several of those examples have not only a geometrical, but also an intriguing aesthetic, aspect. The book addresses high-school students and students at the undergraduate level as well as their teachers, but will appeal to anyone interested in geometry.

In diesem Buch entdecken Sie die mathematischen Muster und Regelmäßigkeiten verschiedener ?Spiralen, Schraubenlinien und spiralartiger Figuren. Deren geometrische Aspekte und Zusammenhänge sind visuell ansprechend aufbereitet und bestmöglich um analytische Aspekte und Darstellungen ergänzt.

Dieses Buch veranschaulicht zentrale mathematische Aspekte des Goldenen Schnittes: Es geht insbesondere auf geometrische und zahlentheoretische Zusammenhänge und Beispiele ein und macht weiterführende Betrachtungen und Verallgemeinerungen zugänglich.Das Buch richtet sich primär an Studierende, Schülerinnen und Schüler, Mathematiklehrpersonen und interessierte Laien. Es ist modular aufgebaut, so dass die einzelnen Kapitel unabhängig voneinander lesbar sind. Die Lektüre soll zu eigenen geometrischen Aktivitäten anregen. Dazu werden auch Tipps und Verfahrenshinweise aus dem handwerklich-kreativen Bereich gegeben.Ergänzende Animationen sind mit der SN More Media App abrufbar: einfach die SN More Media App kostenfrei herunterladen, ein Bild oder einen Link mit dem Play-Button scannen und sofort die Animation auf Smartphone oder Tablet ausspielen.

In this book you will discover the mathematical patterns and regularities of various spirals, helixes and spiral-like figures. Their geometric aspects and connections are presented in a visually appealing way and are supplemented as best as possible with analytical aspects and representations. Using examples from technology and nature, you will learn about round, square, golden and spherical spirals and examine their curvature behavior and other exciting properties. The examples are arranged thematically and the book has a modular structure so that the individual chapters can be read largely independently of each other. It is therefore a valuable resource for students, pupils, (prospective) teachers, those interested in mathematics and those who want to become one.Additional animations are available with the SN More Media app: simply download the SN More Media app free of charge, scan an image or a link with the play button and immediately play the animation on your smartphone or tablet.The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.