Title:
Grade School Triangles
Authors:
Calcut, Jack S.
Abstract:
In grade school, students learn a standard set of Euclidean triangles. Among this set, the usual 45-45-90 and 30-60-90 triangles are the only right triangles with rational angles and side lengths each containing at most one square root. Are there any other such right triangles? We answer this question completely and present an elegant complement called Ailles' rectangle that deserves to be in every geometry teacher's toolkit.
Citation:
Calcut, Jack S. 2010. "Grade School Triangles." American Mathematical Monthly 117(8): 673-685.
Publisher:
Mathematical Association of America
DATE ISSUED:
2010-10
Department:
Mathematics
Type:
article
PUBLISHED VERSION:
10.4169/000298910X515749
PERMANENT LINK:
http://hdl.handle.net/11282/309994

Full metadata record

DC FieldValue Language
dc.contributor.authorCalcut, Jack S.en_US
dc.date.accessioned2013-12-23T16:22:51Z-
dc.date.available2013-12-23T16:22:51Z-
dc.date.issued2010-10en
dc.identifier.citationCalcut, Jack S. 2010. "Grade School Triangles." American Mathematical Monthly 117(8): 673-685.en_US
dc.identifier.issn0002-9890en_US
dc.identifier.urihttp://hdl.handle.net/11282/309994-
dc.description.abstractIn grade school, students learn a standard set of Euclidean triangles. Among this set, the usual 45-45-90 and 30-60-90 triangles are the only right triangles with rational angles and side lengths each containing at most one square root. Are there any other such right triangles? We answer this question completely and present an elegant complement called Ailles' rectangle that deserves to be in every geometry teacher's toolkit.en_US
dc.language.isoen_USen_US
dc.publisherMathematical Association of Americaen_US
dc.identifier.doi10.4169/000298910X515749-
dc.subject.departmentMathematicsen_US
dc.titleGrade School Trianglesen_US
dc.typearticleen_US
dc.identifier.journalAmerican Mathematical Monthlyen_US
dc.subject.keywordMathematicsen_US
dc.identifier.volume117en_US
dc.identifier.issue8en_US
dc.identifier.startpage673en_US
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