Publication at Faculty of Mathematics and Physics |
2015
Abstract
The book presents the shortest constructions of line segments forming the Golden ratio (Divine proportion). It gives the number of steps of the shortest constructions of the Golden Ratio for four types of constructions according the used set of tools: ruler and compass, ruler and collapsible compass, Mohr-Mascheroni (compass only) and collapsible compass only constructions.
The book provides a complete list of these shortest constructions, which are sorted into the classes of similarity. Part of the book is devoted to proofs and geometric principles occurring in these constructions.