Page from Geometria by Augustin Hirschvogel
Hirschvogel (1503–1553), a German artist, mathematician, and cartographer known primarily for his etchings. In this version from the Deutsche Fotothek, amid the rigid lines of the geometrical sketches appear the chaotic forms of stains which lie on each of the pages.
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A star polygon is a non-convex polygon which looks in some way like a star. Only the regular ones have been studied in any depth; star polygons in general appear not to have been formally defined. They should not be confused with star domains.
‘Cyrtoidea’ - Ernst Haeckel, from ‘Kunstformen der Natur’ (1899)
One of my favourites from an incredible book of plates.
Diagrams from Geometrical psychology, or, The science of representation: an abstract of the theories and diagrams of B. W. Betts (1887) by Louisa S. Cook, which details New Zealander Benjamin Bett’s remarkable attempts to mathematically model the evolution of human consciousness through geometric forms. From the Introduction:
“The symbolic forms which Mr. Betts has evolved through his system of Representation resemble, when developed in two dimensions, conventionalised but very scientifically and beautifully conventionalised leaf-outlines. When in more than two dimensions they approximate to the forms of flowers and crystals. …. The fact that he has accidentally portrayed plant-forms when he was studying human evolution is an assurance to Mr. Betts of the fitness of the symbols he has developed, as it affords presumptive evidence that the laws he is studying intuitively admit of universal application.”