Alhazen's circular billiard problem (Q2895469)
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scientific article; zbMATH DE number 6052245
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Alhazen's circular billiard problem |
scientific article; zbMATH DE number 6052245 |
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3 July 2012
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Alhazen's problem
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circular billiard
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0.8858905
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0.82904226
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Alhazen's circular billiard problem (English)
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In this paper simple solutions to two versions of Alhazen's problem are given. The considered problems are:NEWLINENEWLINE- Given a point \(A\) inside a circle, construct points \(B\) and \(C\) on the circle, such that the reflexion of \(AB\) passes through \(C\) and the reflection of \(BC\) passes through \(A\).NEWLINENEWLINE- Given points \(A\) and \(B\) inside a circle, construct a point \(C\) on the circle such that the reflection of \(AC\) passes through \(B\).NEWLINENEWLINEClearly, both problems make sense in the context of ``circular billiards''.NEWLINENEWLINENEWLINEThe given solutions mix both synthetic and analytic ideas, they are elementary and would be suitable (and interesting, I add) to be presented to undergraduates.
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