The buildings gallery: visualizing buildings

Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualizing more complex principles in group theory. As such, they provide an opportunity to talk about the inner workings of mathematics to...

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Published inJournal of mathematics and the arts Vol. 16; no. 1-2; pp. 11 - 28
Main Authors Bekker, Bram, Solleveld, Maarten
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 03.04.2022
Taylor & Francis Ltd
Subjects
Algorithms
Applications programs
BN-pairs
Buildings
geometric group theory
Geometry
Group theory
maths visualization
simplicial complexes
Teaching methods
Three dimensional models
Visualization
Online AccessGet full text
ISSN1751-3472
1751-3480
DOI10.1080/17513472.2022.2063782

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Abstract Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualizing more complex principles in group theory. As such, they provide an opportunity to talk about the inner workings of mathematics to a broader audience, but the visualizations could also serve as a didactic tool in teaching group and building theory, and we believe they can even inspire future research. We present an algorithmic method to visualize these geometric objects. The main accomplishment is the use of existing theory to produce three-dimensional, interactive models of buildings associated with groups with a BN-pair. The final product, an interactive web application called The Buildings Gallery, can be found at https://buildings.gallery/ [Bekker, B. (2021, June). The Buildings Gallery].
AbstractList Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualizing more complex principles in group theory. As such, they provide an opportunity to talk about the inner workings of mathematics to a broader audience, but the visualizations could also serve as a didactic tool in teaching group and building theory, and we believe they can even inspire future research. We present an algorithmic method to visualize these geometric objects. The main accomplishment is the use of existing theory to produce three-dimensional, interactive models of buildings associated with groups with a BN-pair. The final product, an interactive web application called The Buildings Gallery, can be found at https://buildings.gallery/ [Bekker, B. (2021, June). The Buildings Gallery].
Buildings are beautiful mathematical objects tying a variety of subjects in algebra and geometry together in a very direct sense. They form a natural bridge to visualizing more complex principles in group theory. As such, they provide an opportunity to talk about the inner workings of mathematics to a broader audience, but the visualizations could also serve as a didactic tool in teaching group and building theory, and we believe they can even inspire future research. We present an algorithmic method to visualize these geometric objects. The main accomplishment is the use of existing theory to produce three-dimensional, interactive models of buildings associated with groups with a BN-pair. The final product, an interactive web application called The Buildings Gallery, can be found at https://buildings.gallery/ [Bekker, B. (2021, June). The Buildings Gallery].
Author Solleveld, Maarten
Bekker, Bram
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2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This work is licensed under the Creative Commons Attribution – Non-Commercial – No Derivatives License http://creativecommons.org/licenses/by-nc-nd/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
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SubjectTerms Algorithms
Applications programs
BN-pairs
Buildings
geometric group theory
Geometry
Group theory
maths visualization
simplicial complexes
Teaching methods
Three dimensional models
Visualization
Title The buildings gallery: visualizing buildings
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