# The Mysterious Mr. Ammann

@article{Senechal2004TheMM, title={The Mysterious Mr. Ammann}, author={Marjorie Senechal}, journal={The Mathematical Intelligencer}, year={2004}, volume={26}, pages={10-21} }

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…

## 20 Citations

A Summary of the Work of Gregory Margulis

- Mathematics
- 2008

Gregory Margulis is a mathematician of great depth and originality. Besides his celebrated results on super-rigidity and arithmeticity of irreducible lattices of higher rank semisimple Lie groups,…

Mapping the aperiodic landscape, 1982–2007

- Physics
- 2008

The discovery of quasicrystals galvanized mathematics research in long-range aperiodic order, accelerating the dissolution of the the ancient periodic/non-periodic dichotomy begun by Penrose, Ammann,…

Coxeter Pairs, Ammann Patterns and Penrose-like Tilings

- Mathematics, Physics
- 2016

We identify a precise geometric relationship between: (i) certain natural pairs of irreducible reflection groups ("Coxeter pairs"); (ii) self-similar quasicrystalline patterns formed by superposing…

Images of the Ammann-Beenker Tiling

- Mathematics
- 2007

famous, five-fold Penrose rhomb tiling. It was discovered independantly by R. Ammann [AGS02] and F. Beenker [Bee82]. Like the Penrose tiling, the Ammann-Beenker can be constructed by two particular…

A short guide to pure point diffraction in cut-and-project sets

- Physics, Mathematics
- 2016

We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from…

The icosahedral quasiperiodic tiling and its self-similarity

- Mathematics
- 2017

We investigate a 3-dimensional analogue of the Penrose tiling, a class of 3-dimensional aperiodic tilings whose edge vectors are the vertex vectors of a regular icosahedron. It arises by an…

Ammann Tilings in Symplectic Geometry

- Mathematics, Physics
- 2013

In this article we study Ammann tilings from the perspective of symplectic geo- metry. Ammann tilings are nonperiodic tilings that are related to quasicrystals with icosa- hedral symmetry. We…

Self-Similar One-Dimensional Quasilattices

- Mathematics, Physics
- 2016

We study 1D quasilattices, especially self-similar ones that can be used to generate two-, three- and higher-dimensional quasicrystalline tesselations that have matching rules and invertible…

Weak colored local rules for planar tilings

- Computer Science, MathematicsErgodic Theory and Dynamical Systems
- 2019

It is proved that a linear subspace has weak colored local rules if and only if it is computable, including the set of all the linear subspaces of $\mathbb{R}^{n}$ .

Autism and Mathematical Talent

- 2010

A utism is a developmental or personality disorder, not an illness, but autism can coexist with mental illnesses such as schizophrenia and manic-depression. It shows itself in early childhood and is…

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"Remarkable...It will surely remain the unique reference in this area for many years to come." Roger Penrose , Nature "...an outstanding achievement in mathematical education." Bulletin of The London…

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It is well known that there are only three regular polygons that can tile the plane, but here the verb tile means to cover the infinite plane with a set of polygons so that no gaps or overlaps exist among the polygons.

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In 1986 Socolar and Steinhardt introduced a family of quasiperiodic tilings of the euclidean 3-space E3 by four rhombic zonohedra, which admits a local matching rule. In 1989 the first of the present…

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Soon after the announcement of their discovery in 1984 [1], quasi-crystals hit the headlines. Here was a substance—an alloy of aluminum and manganese—whose electron diffraction patterns exhibited…

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Penrose tilings have become the canonical model for quasicrystal structure, primarily because of their simplicity in comparison with other decagonally symmetric quasiperiodic tilings of the plane.…

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Weak matching rules for a quasicrystalline tiling are local rules that ensure that fluctuations in “perp-space” are uniformly bounded. It is shown here that weak matching rules exist forN-fold…

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The cause of autism is mysterious, but genetic factors are important. It takes a variety of forms; the expression autism spectrum, which is often used, gives a false impression that it is just the…