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Leonardo, Vol. 13, pp. 209-210 Pergamon Press, 1980. Printed in Great Britain. COMMENTS ON THE NOTE BY JEAN C. RUSH ON THE APPEAL OF M. C. ESCHER'S PICTURES Michele Emmer* There are some comments I wish to make on the Note by Jean C. Rush in Leonardo [1]. The pictures by M. C. Escher have been made use of in two different ways: (1) to illustrate visual ambiguity in books and articles dealing with different subjects [2, 3] and (2) to illustrate aspects of mathematics, such as symmetry, and nonEuclidean geometry [4-8] and of crystal structures [4, ch. 4, p. 50 and 8]. The article by M. L. Teuber [9] (in the Note by Rush, her Ref. 7, the year of Teuber's article should read 1974, not 1940) provoked a letter to the editor of the Scientific American from Escher's son, George A. Escher [10]. In the letter he said that 'his father's work was not, except in a restricted sense, influenced by the Gestalt psychologist'. Teuber replied: 'In M. C. Escher's case I believe these links can be demonstrated' [10]. Nevertheless, those who knew Escher well are of his son's opinion, and, therefore, the statement by Rush dealing with Teuber's interpretation [1, p. 49] Fig. 1. M. C. Escher. 'Town in Southern Italy', lithographic ink, 62x47, 1929. (Collection of Escher Foundation. Haags Gemeentemuseum, The Hague, Netherlands)·Mathematician, Istituto Matematico G. Castelnuovo, Universita degli studi, Piazzale delle Scienze, 00100 Rome, Italy. (Received 10 Nov. 1979) 209 should be read with awareness of this difference of opinion. Rush states: 'Between 1936 and 1938 Escher abandoned his interest in Italian landscapes and began to make the works for which he is best known' [1 , p. 49]. Actually Escher maintained an interest in the light and shadows of Italian and Mediterranean landscapes after he returned to Holland in 1941. For example, compare the landscapes in his 'Town in Southern Italy' (1936) (Fig. 1) with the background in his picture 'Belvedere' (1958) (Fig. 2). Furthermore, he used aspects of the Fig. 2. M. C. Escher. 'Belvedere', lithograph, 46x29 cm, 1958. (Collection of Escher Foundation. Haags Gemeentemuseum, The Hague, Netherlands) picture painted at Malta entitled 'Senglea' (1935) (Fig. 3) in a few of his pictures involving geometric deformations , as in 'Print Gallery' (1956). As regards the depictions of impossible objects devised by L. S. and R. Penrose reported in 1958 [see 210 Michele Emmer Fig. 3. M. C. Escher. 'Senglea', xylograph, 31 x 46 cm 1935. (Collection of Escher Foundation, Haags Gemeentemusuem, The Hague, Netherlands) Rush, Ref. 9] and Escher's pictures of such objects, I was told the following by R. Penrose during an interview with him in 1979 for a cinema film I was making on mathematical aspects of Escher's works: 'I saw for the first time Escher's works during the 1954 International Mathematics Congress at Amsterdam. I was fascinated particularly by the pictures "Day and Night" (1938) and "Relativity" (1953). When I returned to England, I decided to investigate the possibility of depicting objects with geometrical anomalies that, though not similar to those of Escher's, were also intriguing. I invented the depiction of the impossible solid triangle, and my father, L. S. Penrose, constructed a "real" model of an impossible staircase.' (For a discussion of impossible objects see Ref. li.) In 1958 Escher made his picture 'Belvedere' (Fig. 2) before he received the Penrose's article, mentioned above, containing the drawing of an impossible triangle by R. Penrose. Thus the way to depict an object of the type of an impossible triangle was independently devised by Escher and by R. Penrose. Escher authored a book entitled Periodic Covering of the Plane in 1958 [12], which was not mentioned by Rush. It is well known by mathematicians that there are only 17 possible kinds of symmetry for 2-dimensional geometrical patterns that cover a plane surface [13]. C. H. Macgillavry, while writing her book published in 1965 [Rush's Ref. 10], found that Escher had up to that time used only 15 of the 17 possibilities. She suggested to him that he make a picture for each of the two he...

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