In higher spaces. The path of geometry into the fourth dimension (Q1705184)

Since decades the author has been interested in the subject of higher dimensions; the result is this wonderful book focusing on the second half of the 19th century. The author begins with the 18th century, where there are only few examples; especially Kant is investigated here. In the 19th century, there were several ways of treating the subject of higher dimensions: the ideas according to symmetry led to the application of group theory, the regular polytopes, knots and so on; and of course models play a major role. Many mathematicians contributed to the subject, some of them are not so well known in the history of mathematics. A whole chapter is devoted to Karl Friedrich Zöllner and the scandal he produced by instrumentalizing spiritualistic sessions which took place in Leipzig. The fourth dimension was also treated in literature (Fechner, Abbot, Hinton, Wells) and in art (Duchamp, Bragdon, cubism). Henri Poincaré's contributions were very significant and led among others to the fact, that the fourth dimension lost its fear and just became a more or less usual way of thinking. The book is accompanied by many figures, some of them, especially the very nice portraits, were drawn by Nicola Oswald. The bibliography contains 259 numbers, but the author also mentions archival material. The book is highly recommended for everybody who is interested in the history of geometry. The discussion of the fourth dimension is one of the most fascinating subjects, as a fact and in its time.