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ERIC Number: EJ1093391
Record Type: Journal
Publication Date: 2013
Pages: 19
Abstractor: As Provided
ISSN: ISSN-0819-4564
A Fascinating Application of Steiner's Theorem for Trapezium: Geometric Constructions Using Straightedge Alone
Stupel, Moshe; Ben-Chaim, David
Australian Senior Mathematics Journal, v27 n2 p6-24 2013
Based on Steiner's fascinating theorem for trapezium, seven geometrical constructions using straight-edge alone are described. These constructions provide an excellent base for teaching theorems and the properties of geometrical shapes, as well as challenging thought and inspiring deeper insight into the world of geometry. In particular, this article also mentions the orthic triangle and proves its special property, and shows some other interesting constructions, such as, for example, how to construct a circle's diameter using straightedge alone and having only a segment with its midpoint. In addition, it is enhanced by aspects of the historical background of geometric constructions, including reference to "impossible constructions." Application of the material presented in college or high school can enhance students' appreciation of the elegance, beauty, and fascination of mathematics. Through such "adventures," students will be encouraged to further pursue geometric problems and explore various methods of problem solving, especially those concerned with geometric constructions.
Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education; Postsecondary Education; Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers - Location: Israel
Grant or Contract Numbers: N/A