Find out how to access previewonly content
Date:
15 Nov 2008
The Mysterious Mr. Ammann
 Marjorie Senechal
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
This column is a forum for discussion of mathematical communities throughout the world, and through all time. Our definition of “mathematical community ” is the broadest. We include “schools ” of mathematics, circles of correspondence, mathematical societies, student organizations, and informal communities of cardinality greater than one. What we say about the communities is just as unrestricted. We welcome contributions from mathematicians of all kinds and in all places, and also from scientists, historians, anthropologists, and others.
 The artist is Olafur Eliasson. Einar Thorsteinn supplied this information.
 All letters to and from Martin Gardner quoted in this article, except Ammann ’s first, belong to the Martin Gardner Papers, Stanford University Archives, and are used here with kind permission.
 Gr ünbaum and Shephard preferred the term “aperiodic ” for such tiles. Most authors use the terms “aperiodic ” and “non periodic ” interchangeably.
 John Conway ’s fanciful names —sun, star, king, queen, jack, deuce, and ace —for the seven vertex configurations allowed by Penrose ’s rules seem permanent.
 Ammann, R., Gr, ünbaum, B., , Shephard, G. C. (1992) Aperiodic Tilings. Discrete and Computational Geometry 8: pp. 125 CrossRef
 Martin Gardner ’s chronicles of “Dr. Matrix ” includeThe Incredible Dr. Matrix;The Magic Numbers of Dr. Matrix; andTrapdoors,Ciphers, Penrose Tiles, and the Return of Dr. Matrix.
 Heesch ’s problem asks whether, for each positive integerk, there exists a tile that can be surrounded by copies of itself ink rings, but notk + 1. Such a tile hasHeesch number k. Robert Ammann was the first to find a tile with Heesch number 3. Today tiles with Heesch numbers 4 and 5 are known, but the general problem is still unsolved.
 Hao, Wang (1961) Proving theorems by pattern recognition. II. Bell System Tech. J. 40: pp. 142 CrossRef
 Branko, Grünbaum, Geoffrey, Shephard (1987) Tilings and Patterns. W. H. Freeman, New York
 Martin Gardner, “Extraordinary nonperiodic tiling that enriches the theory of tiles, ” Mathematical Games,Scientific American, January, 1977, 110–121.
 SeeTilings and Patterns, Chapter 10.6, “Ammann bars, musical sequences and forced tiles, ” pp. 571–580.
 Bruijn, N. G. (1981) Algebraic theory of Penrose ’s nonperiodic tilings of the plane. Proceedings of the Koninglike Nederlandse Akademie van Wetenschappen Series A 84: pp. 3866
 M., Senechal, J., Taylor (1990) Quasicrystals: the view from Les Houches. The Mathematical Intelligencer 12: pp. 5464 CrossRef
 Gardner ’s files show that Benoit Mandelbrot met Ammann once in 1980. I had not met Mandelbrot then.
 All letters to and from Branko Gr ünbaum, except my letter after meeting Ammann, are used with Gr ünbaum ’s kind permission.
 Ammann visited and corresponded with Paul Steinhardt and his students, Dov Levine and Joshua Socolar.
 Robert Ammann, “Another Explanation of the CretaceosTertiary Boundary Event, ” unpublished.
 For the journalStructural Topology. The editor, Henry Crapo, also wrote to Ammann about this but also received no reply.
 Roger Penrose, “Remarks on Tiling, ” in R. Moody (ed.),The Mathematics of LongRange Aperiodic Order, Kluwer, 1995, p. 468.
 loan, James (2003) Autism in Mathematics. The Mathematical Intelligencer 25: pp. 6265 CrossRef
 Norbert Wiener,ExProdigy, pp. 3–7, 125–142.
 Conference, “Geometry of Quasicrystals, ” March 1822, 1991, ZIF (Center for Interdisciplinary Research), Bielefeld University, Bielefeld, Germany.
 Joshua, Socolar (1990) Weak Matching Rules for Quasicrystals. Communications in Mathematical Physics 129: pp. 599619 CrossRef
 P., Kramer, R., Neri (1984) On Periodic and Nonperiodic Space Fillings ofE m Obtained by Projection. Acta Crystallographica A40: pp. 580587
 Special Session on Tilings, 868th meeting of the American Mathematical Society, Philadelphia, Pennsylvania, October 12–13, 1991. The American Mathematical Society does not pay honoraria or travel expenses.
 At the last minute Coxeter couldn ’t come. They never met.
 H. Williams, “Richland Lad, 3, is Wizard at Geography, ”The Herald (Richland, Washington), 1949 (undated clipping). The Ammann family had moved from Massachusetts to Washington while August Ammann, an engineer, worked on a nuclear power construction project there.
 Title
 The Mysterious Mr. Ammann
 Journal

The Mathematical Intelligencer
Volume 26, Issue 4 , pp 1021
 Cover Date
 20040901
 DOI
 10.1007/BF02985414
 Print ISSN
 03436993
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Industry Sectors
 Authors

 Marjorie Senechal ^{(1)}
 Author Affiliations

 1. Department of Mathematics, Smith College, 01063, Northampton, MA, USA