Il y a des mathématiciens niveau DEUG MASS qui imaginent leurs fantasmes derrière Prentententoonstelling, il y a des mathématiciens qui la remplissent.
Honte au premier, honneur aux seconds. Enjoy!
Pari raté (#1) pour Jean Staune.
Artful Mathematics: The Heritage of M. C. Escher [direct pdf link]
The Mathematical Structure of Escher’s Print Gallery
B. de Smit and H. W. Lenstra J
Notices of the AMS, April 2003 Volume 50 Issue 4
In 1956 the Dutch graphic artist Maurits Cornelis Escher (1898–1972) made an unusual lithograph with the title Prentententoonstelling. It shows a young man standing in an exhibition gallery, viewing a print of a Mediterranean seaport. As his eyes follow the quayside buildings shown on the print from left to right and then down, he discovers among them the very same gallery in which he is standing. A circular white patch in the middle of the lithograph contains Escher’s monogram and signature.
What is the mathematics behind Prentententoonstelling? Is there a more satisfactory way of filling in the central white hole? We shall see that the lithograph can be viewed as drawn on a certain elliptic curve over the field of complex numbers and deduce that an idealized version of the picture repeats itself in the middle. More precisely, it contains a copy of itself, rotated clockwise by 157.6255960832… degrees and scaled down by a factor of 22.5836845286…