The three Steiner-Lehmus theorems
Steiner’s proof of what is now called the Steiner-Lehmus theorem was published in 1844, the same year as the book The three musketeers , written by the French author Alexandre Dumas. The motto One for all, all for one (Einer für alle, alle für einen; Un pour tous, tous pour un; Uno per tutti, tutti...
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Cambridge University Press (CUP)
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crcambridgeupr:10.1017/mag.2019.61 2024-03-03T08:36:29+00:00 The three Steiner-Lehmus theorems Beardon, A. F. 2019 http://dx.doi.org/10.1017/mag.2019.61 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0025557219000615 en eng Cambridge University Press (CUP) https://www.cambridge.org/core/terms The Mathematical Gazette volume 103, issue 557, page 293-304 ISSN 0025-5572 2056-6328 General Mathematics journal-article 2019 crcambridgeupr https://doi.org/10.1017/mag.2019.61 2024-02-08T08:25:59Z Steiner’s proof of what is now called the Steiner-Lehmus theorem was published in 1844, the same year as the book The three musketeers , written by the French author Alexandre Dumas. The motto One for all, all for one (Einer für alle, alle für einen; Un pour tous, tous pour un; Uno per tutti, tutti per uno) of the three musketeers came into widespread use in Europe in the 19th century, and its essence is that the three musketeers are inseparable; each member pledges to support the group, and the group supports each member. Now there are three classical geometries of constant curvature, namely Euclidean, spherical and hyperbolic geometries, and one can argue that, like the three musketeers, these geometries should be considered as being inseparable; that is, an idea, theorem or proof in any one of them should automatically be considered in the other two. The issue here should be not only to decide whether a particular result is true, or false, in a given geometry, but to understand which particular properties of the geometries make it so . Article in Journal/Newspaper Alle alle Cambridge University Press The Mathematical Gazette 103 557 293 304 |
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General Mathematics |
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General Mathematics Beardon, A. F. The three Steiner-Lehmus theorems |
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General Mathematics |
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Steiner’s proof of what is now called the Steiner-Lehmus theorem was published in 1844, the same year as the book The three musketeers , written by the French author Alexandre Dumas. The motto One for all, all for one (Einer für alle, alle für einen; Un pour tous, tous pour un; Uno per tutti, tutti per uno) of the three musketeers came into widespread use in Europe in the 19th century, and its essence is that the three musketeers are inseparable; each member pledges to support the group, and the group supports each member. Now there are three classical geometries of constant curvature, namely Euclidean, spherical and hyperbolic geometries, and one can argue that, like the three musketeers, these geometries should be considered as being inseparable; that is, an idea, theorem or proof in any one of them should automatically be considered in the other two. The issue here should be not only to decide whether a particular result is true, or false, in a given geometry, but to understand which particular properties of the geometries make it so . |
format |
Article in Journal/Newspaper |
author |
Beardon, A. F. |
author_facet |
Beardon, A. F. |
author_sort |
Beardon, A. F. |
title |
The three Steiner-Lehmus theorems |
title_short |
The three Steiner-Lehmus theorems |
title_full |
The three Steiner-Lehmus theorems |
title_fullStr |
The three Steiner-Lehmus theorems |
title_full_unstemmed |
The three Steiner-Lehmus theorems |
title_sort |
three steiner-lehmus theorems |
publisher |
Cambridge University Press (CUP) |
publishDate |
2019 |
url |
http://dx.doi.org/10.1017/mag.2019.61 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0025557219000615 |
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Alle alle |
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Alle alle |
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The Mathematical Gazette volume 103, issue 557, page 293-304 ISSN 0025-5572 2056-6328 |
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https://www.cambridge.org/core/terms |
op_doi |
https://doi.org/10.1017/mag.2019.61 |
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The Mathematical Gazette |
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103 |
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557 |
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293 |
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