A remark on the Beckman/Quarles theorem (Q1377798)
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scientific article; zbMATH DE number 1110056
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A remark on the Beckman/Quarles theorem |
scientific article; zbMATH DE number 1110056 |
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A remark on the Beckman/Quarles theorem (English)
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26 January 1998
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The author studies the Beckman-Quarles theorem in euclidean planes. Combining a series of results of other geometers (also with reference to T. R. Dawson's ``match-stick'' geometry, which was recently popularized again in a chapter of G. E. Martin's new book about geometric constructions) he obtains the following Corollary: Let \(f\) be a bijection of a euclidean plane over an archimedean field that preserves a constant distance between points and lines. Then \(f\) is an isometry.
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archimedean plane
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\(k\)-homometry
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Beckman-Quarles theorem
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isometry
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