Robert Ammann
Encyclopedia
Robert Ammann was an amateur mathematician who made several significant and groundbreaking contributions to the theory of quasicrystal
s and aperiodic tiling
s.
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 a post office
.
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.
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 quasicrystal
s in 1982 changed the status of aperiodic tilings and Ammann's work from mere recreational mathematics
to respectable academic research.
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 Tilings and Patterns and later, in collaboration with the authors of the book, he published a paper 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 which became known as the Ammann–Beenker tiling
. In 1987 Wang, Chen and Kuo announced the discovery of a quasicrystal with octagonal symmetry .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 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.
Quasicrystal
A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry...
s and aperiodic tiling
Aperiodic tiling
An aperiodic tiling is a tiling obtained from an aperiodic set of tiles. Properly speaking, aperiodicity is a property of particular sets of tiles; any given finite tiling is either periodic or non-periodic...
s.
Brandeis University
Brandeis University is an American private research university with a liberal arts focus. It is located in the southwestern corner of Waltham, Massachusetts, nine miles west of Boston. The University has an enrollment of approximately 3,200 undergraduate and 2,100 graduate students. In 2011, it...
, but generally did not go to classes, and left after three years. He worked as a programmer
Programmer
A programmer, computer programmer or coder is someone who writes computer software. The term computer programmer can refer to a specialist in one area of computer programming or to a generalist who writes code for many kinds of software. One who practices or professes a formal approach to...
for Honeywell
Honeywell
Honeywell International, Inc. is a major conglomerate company that produces a variety of consumer products, engineering services, and aerospace systems for a wide variety of customers, from private consumers to major corporations and governments....
. After ten years, his position was eliminated as part of a routine cutback, and Ammann ended up working as a mail sorter for a post office
Post office
A post office is a facility forming part of a postal system for the posting, receipt, sorting, handling, transmission or delivery of mail.Post offices offer mail-related services such as post office boxes, postage and packaging supplies...
.
In 1975, Ammann read an announcement by Martin Gardner
Martin Gardner
Martin Gardner was an American mathematics and science writer specializing in recreational mathematics, but with interests encompassing micromagic, stage magic, literature , philosophy, scientific skepticism, and religion...
of new work by Roger Penrose
Roger Penrose
Sir Roger Penrose OM FRS 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...
. Penrose had discovered two simple sets of aperiodic tiles, each consisting of just two quadrilaterals. Since Penrose was taking out a patent
Patent
A patent is a form of intellectual property. It consists of a set of exclusive rights granted by a sovereign state to an inventor or their assignee for a limited period of time in exchange for the public disclosure of an invention....
, 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.
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 quasicrystal
Quasicrystal
A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry...
s in 1982 changed the status of aperiodic tilings and Ammann's work from mere recreational mathematics
Recreational mathematics
Recreational mathematics is an umbrella term, referring to mathematical puzzles and mathematical games.Not all problems in this field require a knowledge of advanced mathematics, and thus, recreational mathematics often attracts the curiosity of non-mathematicians, and inspires their further study...
to respectable academic research.
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 Tilings and Patterns and later, in collaboration with the authors of the book, he published a paper 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
Nicolaas Govert de Bruijn
Nicolaas Govert de Bruijn is a Dutch mathematician, affiliated as professor emeritus with the Eindhoven University of Technology. He received his Ph.D. in 1943 from Vrije Universiteit Amsterdam....
exposed the cut and project method and in 1984 came the sensational news about Shechtman quasicrystal which promoted the Penrose tiling
Penrose tiling
A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original...
to fame. But in 1982 Beenker published a similar mathematical explanation for the octagonal case which became known as the Ammann–Beenker tiling
Ammann–Beenker tiling
In geometry, an Ammann–Beenker tiling is a nonperiodic tiling generated by an aperiodic set of prototiles named after Robert Ammann, who first discovered the tilings in the 1970s, and after F. P. M...
. In 1987 Wang, Chen and Kuo announced the discovery of a quasicrystal with octagonal symmetry .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 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.