Hans Walser, a former high school teacher and lecturer at ETH Zurich, the University of Basel and the University of Basel Education, compiled a 155-page paperback about spirals and spirals from a variety of his materials. Anyone who has seen Walser in a lecture above all will likely remember that one is almost “overwhelmed” by the multitude of ideas presented and the wealth of color images on display: what is presented undoubtedly stimulates thought. However, you can rarely do this during a lecture, because the next drawing or the next sequence of pictures follows.
Take up the topic of spirals again
After – especially for the implementation of the topic in the classroom or in teacher training – Very useful book “Spiralen” by Jonah Heitzer from 1998Unfortunately, it’s out of print, it’s time to rework the topic. In this regard, one can only hope that many mathematics students, talented students, teachers, and those interested in mathematics will purchase and work on this inspiring book. Because browsing the papers is not enough, even if the photos and photo sequences are a feast for the eyes.
The work is divided into ten chapters, which – after an introduction to the first chapter – can be read almost independently of one another. It concerns first the logarithmic and arithmetic spirals, then about screws, angular (logarithmic and arithmetic) spirals, about golden spirals and about spherical spirals (with a digression on geographical maps). Two chapters deal with felt cloth and wavy lines respectively. Walser also deals with optical illusions in helix-like shapes.
The book flourishes with more than 250 color drawings that Walser uses to illustrate the facts presented, including wonderful color images of spirals in nature or in architecture. However, graphics arrangement suffers somewhat from the publisher’s strict layout rules, according to which graphics can appear only at the top or bottom of a page. As a result, always pay close attention to the numbering of the illustrations when reading and turning the pages frequently.
The book’s supplemental material contains 28 web links to great, if not quite technically mature, animations: videos of animated characters or advanced structures. Unfortunately, two links don’t work, but you can also find the videos under the thumbnails on Walser (The animation is of much better quality there).
Valser is the master of difference, as proves in this book. His website contains hundreds of so-called “miniatures” (as he humbly calls them), including many photos on the topic of spirals. He was not able to include all contributions in his book, ie no comments on n-angled spirals and their lengths. But maybe that could be added in the second edition.
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