Robert Ammann (October 1, 1946 - May, 1994) was an amateur mathematician who made several significant and groundbreaking contributions to the theory of quasicrystals and aperiodic tilings. is the 274th day of the year (275th in leap years) in the Gregorian calendar. ... Year 1946 (MCMXLVI) was a common year starting on Tuesday (link will display full 1946 calendar) of the Gregorian calendar. ... Year 1994 (MCMXCIV) The year 1994 was designated as the International Year of the Family and the International Year of the Sport and the Olympic Ideal by the United Nations. ... This is a list of people whose primary vocation did not involve mathematics (or any similar discipline) yet made notable, and sometimes important, contributions to the field of mathematics. ... Quasicrystals are aperiodic structures which produce diffraction. ... This article or section is in need of attention from an expert on the subject. ...

Ammann-Beenker tiling.

Ammann attended Brandeis University, but generally did not go to classes, and left after three years. He worked as a programmer for Honeywell. After ten years, his position was eliminated as part of a routine cutback, and Ammann ended up working as a mail sorter for the post office. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Brandeis University is a private university located in Waltham, Massachusetts, United States. ... Honeywell Heating Specialties Company Stock Certificate dated 1924 signed by Mark C. Honeywell - courtesy of Scripophily. ...

In 1975, Ammann read an announcement by Martin Gardner of new work by Roger Penrose. Penrose had discovered two simple sets of aperiodic tiles, each consisting of just two quadrilaterals. Since Penrose was taking out a patent, he wasn't ready to publish them, and Gardner's description was rather vague. Ammann wrote a letter to Gardner, describing his own work, which duplicated one of Penrose's sets, plus a foursome of "golden rhombohedra" that formed aperiodic tilings in space. Year 1975 (MCMLXXV) was a common year starting on Wednesday (link will display full calendar) of the Gregorian calendar. ... Martin Gardner (b. ... Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. ...

More letters followed, and Ammann became a correspondent with many of the professional researchers. He discovered several new aperiodic tilings, each among the simplest known examples of aperiodic sets of tiles. He also showed how to generate tilings using lines in the plane as guides for lines marked on the tiles, now called "Ammann bars".

The discovery of quasicrystals in 1982 changed the status of aperiodic tilings and Ammann's work from mere recreational mathematics to respectable academic research. Quasicrystals are aperiodic structures which produce diffraction. ... Recreational mathematics includes many mathematical games, and can be extended to cover such areas as logic and other puzzles of deductive reasoning. ...

After more than ten years of coaxing, he agreed to meet various professionals in person, and eventually even went to two conferences and delivered a lecture at each. Afterwards, Ammann dropped out of sight, and died of a heart attack a few years later. News of his death did not reach the research community for a few more years.

Five sets of tiles discovered by Ammann were described in Tillings and Patterns^[1] and later, in collaboration with the authors of the book, he published a paper^[2] proving the aperiodicity for four of them. Ammann's discoveries came to notice only after Penrose had published his own discovery and gained priority. In 1981 de Bruijn exposed the cut and project method and in 1984 came the sensational news about Shechtman quasicrystal which promoted the Penrose tiling to fame. But in 1982 Beenker published a similar mathematical explanation for the octagonal case ^[3] which became known as the Ammann-Beenker tiling. In 1987 Wang, Chen and Kuo announced the discovery of a quasicrystal with octagonal symmetry ^[4].The decagonal covering of the Penrose tiling was proposed in 1996 and two years later F. Gahler proposed an octagonal variant for the Ammann-Beenker tiling^[5] Ammann's name became that of the perennial second. It is acknowledged however that Robert Ammann first proposed the construction of rhombic prisms which is the three-dimensional model of Shechtman's quasicrystals. A Penrose tiling A Penrose tiling is an aperiodic tiling of the plane discovered by Roger Penrose in 1973. ...

References and Notes

1. ^ B. Grunbaum and G.C. Shephard, Tilings and Patterns, Freemann, NY 1986
2. ^ R.Ammann, B. Grunbaum and G.C. Shephard, Aperiodic Tiles, Discrete Comput Geom 8 (1992),1-25
3. ^ Beenker FPM, Algebric theory of non periodic tilings of the plane by two simple building blocks: a square and a rhombus, TH Report 82-WSK-04 (1982), Technische Hogeschool, Eindhoven
4. ^ Wang N., Chen H. and Kuo K., Phys Rev Lett. 59(1987) 1010
5. ^ S. Ben Abraham and F. Gahler, Phys. Rev. B60(1999)860

• Senechal, Marjorie, "The Mysterious Mr. Ammann", The Mathematical Intelligencer, 26:4 (2004).
• Amman tilings and references at the Tilings encyclopedia