1 Introduction -- 2 The logarithmic spiral -- 3 The Archimedean spiral -- 4 Screws -- 5 Angular logarithmic spirals -- 6 Angular Archimedean spirals -- 7 Curvature -- 8 Golden spirals -- 9 Optical illusions -- 10 Spherical spirals.

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. The Author Dr. Hans Walser was a high school teacher and lecturer at the ETH Zurich, the University of Basel and the Basel University of Education in the areas of teacher training and mathematics for natural and engineering students.