A proposition from algebra – how would Pythagoras phrase it?

Moshe Stupel, Avi Sigler

Abstract


The paper presents three methods from different branches of mathematics for the solution of the same task. Originally this is an algebraic problem, and therefore the first solution presented is the one utilizing the algebraic method. Subsequently, the question was “translated” into a geometric language, with an “interesting” presentation of the problem – “how would Pythagoras phrase and solve the problem?” Later, we bring the geometric and trigonometric solution deal with a special triangle whose angles are a, 2a, 4a – a geometric progression. Solution of the same problem using different methods contributes to the enrichment of the “mathematical toolbox” of the student and exemplifies to the student the beauty of mathematics as a field composed of intertwining branches.


Full Text:

PDF

References


Ersoz, F.A.: 2009, ‘Proof in different mathematical domains’, ICME Study, Vol. 1, pp. 160-165.

Hardy, G. H. :1940. A mathematicians apology. Cambridge, UK: Cambridge University Press , p.40.

Levav-Waynberg, A. and Leikin, R.: 2009, ‘Multiple solutions for a problem: A tool for evaluation of mathematical thinking in geometry’, In Proceedings of CERME 6, January 28th - February 1st 2009, Lyon, France, pp. 776-785.

Liekin, R. and Lev H.: 2007, ‘Multiple solution tasks as a magnifying glass for observation of mathematical creativity’, In J.H. Wo, H.C. Lew, K.S. Park and D.Y. Seo (eds.), Proceedings of the 31st International Conference for the Psychology of Mathematics Education. Vol. 3, The Korea Society of Educational Studies in Mathematics, Korea, pp. 161-168.

Liekin, R.: 2009, ‘Multiple proof tasks: Teacher practice and teacher education’, ICME Study 19, Vol. 2, pp. 31-36.

Liekin, R. and Lev H.: 2007, ‘Multiple solution tasks as a magnifying glass for observation of mathematical creativity’, In J.H. Wo, H.C. Lew, K.S. Park and D.Y. Seo (eds.), Proceedings of the 31st International Conference for the Psychology of Mathematics Education. Vol. 3, The Korea Society of Educational Studies in Mathematics, Korea, pp. 161-168.

National Council of Teachers of Mathematics: 2000, Principles and standards for school mathematics, NCTM, Reston, VA.

Polya, G.: 1973, How to Solve It: A New Aspect of Mathematical Method, Princeton University Press, Princeton, NJ.

Schoenfeld, A.H.: 1985, Mathematical Problem Solving, Academic Press, New York.

Schoenfeld, A.H.: 1988, ‘When good teaching leads to bad results: The disasters of “well-taught” mathematics courses’, Educational Psychologist, 23 (2), 145-166.

Stupel, M, & Ben-Chaim, D. : 2013. One problem, multiple solutions: How multiple proofs can connect several areas of mathematics. Far East Journal of Mathematical Education. Vol. 11(2), pp. 129-161.

Tall, D.: 2007, ‘Teachers as Mentors to encourage both power and simplicity in active material learning’, Plenary Lecture at the Third Annual Conference for Middle East Teachers of Science, Mathematics and Computing, 17-19, March 2007, Abu-Dhabi.


Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Moshe Stupel, Avi Sigler

The Ohio Journal of School Mathematics is published by the Ohio Council of Teachers of Mathematics and hosted by The Ohio State University Libraries.

If you encounter problems with the site or have comments to offer, including any access difficulty due to incompatibility with adaptive technology, please contact libkbhelp@lists.osu.edu.

ISSN 2472-5986 (print)
ISSN 2472-601X (online)