Robert Ammann (October 1, 1946 – May, 1994) was an amateur mathematician who made several significant and groundbreaking contributions to the theory of

quasicrystal A quasiperiodic crystal, or quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. While crystals, according to the classical ...

s and

aperiodic tiling An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non- peri ...

s. Ammann attended

Brandeis University , mottoeng = "Truth even unto its innermost parts" , established = , type = Private research university , accreditation = NECHE , president = Ronald D. Liebowitz , ...

, but generally did not go to classes, and left after three years. He worked as a programmer for

Honeywell Honeywell International Inc. is an American publicly traded, multinational conglomerate corporation headquartered in Charlotte, North Carolina. It primarily operates in four areas of business: aerospace, building technologies, performance ma ...

. 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 A post office is a public facility and a retailer that provides mail services, such as accepting letters and parcels, providing post office boxes, and selling postage stamps, packaging, and stationery. Post offices may offer additional ser ...

. In 1975, Ammann read an announcement by

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lew ...

of new work by Roger Penrose. Penrose had discovered two simple sets of aperiodic tiles, each consisting of just two

quadrilaterals In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, ...

. Since Penrose was taking out a

patent A patent is a type of intellectual property that gives its owner the legal right to exclude others from making, using, or selling an invention for a limited period of time in exchange for publishing an enabling disclosure of the invention."A ...

, 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 Ammann is a surname of German origin which is an alternative spelling of Amtmann or Amman, an historical kind of bailiff. Notable people with the surname include: *Alberto Ammann, Argentine actor *Daniel Ammann, Swiss author and journalist (born 19 ...

". The discovery of

s in 1982 changed the status of aperiodic tilings and Ammann's work from mere

recreational mathematics Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...

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 quasicrystals which promoted the

Penrose tiling A Penrose tiling is an example of an aperiodic tiling. Here, a ''tiling'' is a covering of the plane by non-overlapping polygons or other shapes, and ''aperiodic'' means that shifting any tiling with these shapes by any finite distance, without ...

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 Ben Abraham and Gähler proposed an octagonal variant for the Ammann–Beenker tiling. Ammann's name became that of the perennial second. It is acknowledged however that Ammann first proposed the construction of rhombic prisms which is the three-dimensional model of Shechtman's quasicrystals.

References

External links

* Ammann tilings and references at th
Tilings encyclopedia
* {{DEFAULTSORT:Ammann, Robert Amateur mathematicians Recreational mathematicians 20th-century American mathematicians 1946 births 1994 deaths Brandeis University alumni