Aunt Alice in Wonderland

2020 ◽  
pp. 211-222
Author(s):  
Nicholas Mee
Keyword(s):  
Twentieth Century ◽  
Three Dimensional ◽  
Formal Training ◽  
Regular Polytopes ◽  
Platonic Solids ◽  
Alice In Wonderland ◽  
Dutch Mathematician

George and Mary Everest Boole’s daughter Alicia learnt Hinton’s methods for visualizing hypercubes during her teens and developed an incredible facility for four-dimensional geometry. As a housewife and without any formal training in mathematics she discovered all six regular four-dimensional polytopes (the four-dimensional Platonic solids) and made models of their three-dimensional sections. The regular polytopes had previously been discovered by Ludwig Schläfli and William Irving Stringham, but their work had received little attention and was probably unknown to Alicia Stott Boole. Alicia later worked for a time with the Dutch mathematician Pieter Hendrik Schoute. When she was in her 70s, her nephew, later Professor Geoffrey Ingram Taylor, introduced her to a young Cambridge student called Donald Coxeter. Coxeter developed her ideas further, and in 1948 published the first edition of his book Regular Polytopes. Coxeter is now recognized as the greatest classical geometer of the twentieth century.

Reading the Image of Race: Neurocriminology, Medical Imaging Technologies and Literary Intervention

2018 ◽  
Author(s):  
Lindsey Andrews ◽  
Jonathan M. Metzl
Keyword(s):  
Twentieth Century ◽  
Wall Street Journal ◽  
Genetic Basis ◽  
Three Dimensional ◽  
Criminal Behaviour ◽  
Dominant Model ◽  
Wall Street ◽  
Behavioural Genetics ◽  
Black And White ◽  
Brain Scan

On 26 April 2013, the Wall Street Journal published an essay by neurocriminologist Adrian Raine promoting his newest book, The Anatomy of Violence: The Biological Roots of Crime. On the newspaper’s website, an image of a black-and-white brain scan overlaid with handcuffs headed the essay. Clicking ‘play’ turned the image into a video filled with three-dimensional brain illustrations and Raine’s claims that some brains are simply more biologically prone to violence than others. Rejecting what he describes as ‘the dominant model for understanding criminal behaviour in the twentieth century’ – a model based ‘almost exclusively on social and sociological’ explanations – Raine wrote that ‘the genetic basis of criminal behaviour is now well established’ through molecular and behavioural genetics.

Two Centuries of Excavating Merovingian-Era Cemeteries In France

2020 ◽  
pp. 76-95
Author(s):  
Bonnie Effros
Keyword(s):  
Twentieth Century ◽  
Ethnic Identity ◽  
Central Place ◽  
State Funding ◽  
Formal Training ◽  
Negative Consequences ◽  
Private Funding ◽  
Research Questions ◽  
The Creation

The excavation of Merovingian-period cemeteries in France began in earnest in the 1830s spurred by industrialization, the creation of many new antiquarian societies across the country, and French nationalism. However, the professionalization of the discipline of archaeology occurred slowly due to the lack of formal training in France, weak legal protections for antiquities, and insufficient state funding for archaeological endeavors. This chapter identifies the implications of the central place occupied by cemeterial excavations up until the mid-twentieth century and its impact on broader discussions in France of national origins and ethnic identity. In more recent years, with the creation of archaeological agencies such as Afan and Inrap, the central place once occupied by grave remains has been diminished. Rescue excavations and private funding for new structures have brought about a shift to other priorities and research questions, with both positive and negative consequences, though cemeteries remain an important source of evidence for our understanding of Merovingian society.

scholarly journals Representing the War. Early Twentieth Century Maps and Models in the Fonds of the Italian War History Museum in Rovereto

2021 ◽  
Vol 4 ◽  
pp. 1-8
Author(s):  
Elena Dai Prà ◽  
Valentina De Santi ◽  
Giannantonio Scaglione
Keyword(s):  
Twentieth Century ◽  
Three Dimensional ◽  
Field Surveys ◽  
History Museum ◽  
Early Twentieth Century ◽  
Wide Range ◽  
The First World War ◽  
Three Dimensional Models ◽  
The University ◽  
First World

Abstract. The representation of the areas in which some of the most significant events of the First World War took place has produced a wide range of materials, such as cartography, aerial and terrestrial photos, textual descriptions and field surveys. In addition, war events were also represented through three-dimensional models. Topographic maps and models constitute composite figurations, which are rich in informative data useful for the preservation of the memory of places and for increasing the knowledge of cultural heritage. Hence, these sources need to be studied, described, interpreted and used for future enhancement. The focus of this paper are archival materials from the collections kept at the Italian War History Museum of Rovereto (Museo Storico Italiano della Guerra), in the Trentino-Alto Adige region. Firstly, we will investigate the cartographic fond in order to assess the composition and origin of its materials. Secondly, we will present the Museum’s collection of Early-Twentieth Century models. Such precious heritage is not yet part of an exhibition, and is kept in the Museum’s warehouses. The paper constitutes the occasion to present the initial results of a still ongoing project by the Geo-Cartographic Centre for Study and Documentation (GeCo) of the University of Trento on the study and analysis of two archival complexes preserved in the abovementioned Museum. In particular, the paper focuses on the heuristic value of such representational devices, which enable an analysis of the different methods and languages through which space is planned and designed, emphasizing the complementarity between different types of visualization.

scholarly journals Platonic solids generate their four-dimensional analogues

2013 ◽  
Vol 69 (6) ◽  
pp. 592-602 ◽  
Author(s):  
Pierre-Philippe Dechant
Keyword(s):  
Coxeter Groups ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Root Systems ◽  
Point Of View ◽  
Platonic Solids ◽  
Four Dimensions ◽  
Potential Applications ◽  
Regular Convex ◽  
Quasi Crystals

This paper shows how regular convex 4-polytopes – the analogues of the Platonic solids in four dimensions – can be constructed from three-dimensional considerations concerning the Platonic solids alone.Viathe Cartan–Dieudonné theorem, the reflective symmetries of the Platonic solids generate rotations. In a Clifford algebra framework, the space of spinors generating such three-dimensional rotations has a natural four-dimensional Euclidean structure. The spinors arising from the Platonic solids can thus in turn be interpreted as vertices in four-dimensional space, giving a simple construction of the four-dimensional polytopes 16-cell, 24-cell, theF4root system and the 600-cell. In particular, these polytopes have `mysterious' symmetries, that are almost trivial when seen from the three-dimensional spinorial point of view. In fact, all these induced polytopes are also known to be root systems and thus generate rank-4 Coxeter groups, which can be shown to be a general property of the spinor construction. These considerations thus also apply to other root systems such as A_{1}\oplus I_{2}(n) which induces I_{2}(n)\oplus I_{2}(n), explaining the existence of the grand antiprism and the snub 24-cell, as well as their symmetries. These results are discussed in the wider mathematical context of Arnold's trinities and the McKay correspondence. These results are thus a novel link between the geometries of three and four dimensions, with interesting potential applications on both sides of the correspondence, to real three-dimensional systems with polyhedral symmetries such as (quasi)crystals and viruses, as well as four-dimensional geometries arising for instance in Grand Unified Theories and string and M-theory.

scholarly journals Faraday instability on a sphere: numerical simulation

2019 ◽  
Vol 870 ◽  
pp. 433-459 ◽  
Author(s):  
A. Ebo-Adou ◽  
L. S. Tuckerman ◽  
S. Shin ◽  
J. Chergui ◽  
D. Juric
Keyword(s):  
Body Force ◽  
Three Dimensional ◽  
Capillary Waves ◽  
Platonic Solids ◽  
Interface Motion ◽  
Spherical Drop ◽  
Low Viscosity ◽  
Faraday Instability ◽  
Viscous Drop ◽  
Time Periodic

We consider a spherical variant of the Faraday problem, in which a spherical drop is subjected to a time-periodic body force, as well as surface tension. We use a full three-dimensional parallel front-tracking code to calculate the interface motion of the parametrically forced oscillating viscous drop, as well as the velocity field inside and outside the drop. Forcing frequencies are chosen so as to excite spherical harmonic wavenumbers ranging from 1 to 6. We excite gravity waves for wavenumbers 1 and 2 and observe translational and oblate–prolate oscillation, respectively. For wavenumbers 3 to 6, we excite capillary waves and observe patterns analogous to the Platonic solids. For low viscosity, both subharmonic and harmonic responses are accessible. The patterns arising in each case are interpreted in the context of the theory of pattern formation with spherical symmetry.

Triangulations and meshes in computational geometry

Acta Numerica ◽  
2000 ◽  
Vol 9 ◽  
pp. 133-213 ◽  
Author(s):  
Herbert Edelsbrunner
Keyword(s):  
Twentieth Century ◽  
Computational Geometry ◽  
Delaunay Triangulation ◽  
Mesh Generation ◽  
Three Dimensional ◽  
Central Theme ◽  
Physical Processes ◽  
Finite Point ◽  
Major Application ◽  
Point Set

The Delaunay triangulation of a finite point set is a central theme in computational geometry. It finds its major application in the generation of meshes used in the simulation of physical processes. This paper connects the predominantly combinatorial work in classical computational geometry with the numerical interest in mesh generation. It focuses on the two- and three-dimensional case and covers results obtained during the twentieth century.

The reinvention of twentieth century microscopy for three‐dimensional imaging

2017 ◽  
Vol 95 (6) ◽  
pp. 520-524 ◽  
Author(s):  
Lachlan W Whitehead ◽  
Kate McArthur ◽  
Niall D Geoghegan ◽  
Kelly L Rogers
Keyword(s):  
Twentieth Century ◽  
Three Dimensional ◽  
Three Dimensional Imaging

“Smooth Space” for Avatars

2015 ◽  
pp. 26-38
Author(s):  
Elif Ayiter
Keyword(s):  
Twentieth Century ◽  
Literature Review ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Digital Artifact ◽  
Smooth Space

During the years of Suprematism, between 1919 and 1923 in Russia, one of the movement's most significant contributors, architect, artist and designer El Lissitzky developed a series of works which he entitled “Prouns,” a name the exact meaning of which El Lissitzky never fully revealed, although he later described the purpose of his creations as interchange stations from painting to architecture, i.e., from two dimensional to three dimensional visuality. The author has re-created El Lissitzky's “Proun #5A” from 1919 in the metaverse, as an architecture for avatars. The process in which the translation from analogue drawing to three dimensional digital artifact was undertaken, the challenges encountered during its re-building; framed within a literature review that examines both El Lissitzky's influence on contemporary cyber-architecture, as well as the significance of his spatial investigations and his sources of inspiration during the early decades of the twentieth century will form the contents of this text.

The Hut-Hospital as Project and as Practice

2018 ◽  
Vol 62 (2) ◽  
pp. 76-97 ◽  
Author(s):  
Cristiana Bastos
Keyword(s):  
Twentieth Century ◽  
Indigenous Population ◽  
Three Dimensional ◽  
Indigenous Populations ◽  
Medical Assistance ◽  
Legal Documents ◽  
History Of ◽  
Conference Papers ◽  
Plaster Models ◽  
Different Sources

This article analyzes one kind of colonial equipment designed in the early twentieth century for the purpose of providing medical assistance to the indigenous populations of Angola and Mozambique. I will refer to it as a ‘hut-hospital’, although it had several forms and designations. The layout of hut-hospitals consisted of a main building and a number of hut-like units that were supposedly more attractive to the indigenous population and therefore more efficient than the large, rectangular buildings of the main colonial hospitals. Using different sources, including three-dimensional plaster models of hut-hospitals, photographs, legal documents, and 1920s conference papers and articles, I will investigate the relatively obscure history of this colonial artifact while exploring the use of imitation as part of the repertoire of colonial governance.

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