A new look at an old triangle counting problem

• Autores: Tim J. McDevitt, Kathryn Sutcliffe, Brian M. Dean (ed. lit.), Daniel Ness (ed. lit.), Nick Wasserman (ed. lit.)
• Localización: Mathematics teacher, ISSN-e 2330-0582, ISSN 0025-5769, Vol. 110, Nº 6, 2017, págs. 470-474
• Idioma: inglés
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• Resumen

  • The correct answer to the problem in figure 1 is 15. There are nine triangles congruent to ABE, three triangles congruent to ACH, two triangles congruent to BGH, plus ADJ, for a total of 15 equilateral triangles. Co-author Sutcliffe recently encountered this problem on a MATHCOUNTS® poster titled “What number do the following have in common” in her high school classroom while student teaching, and the problem generated a great deal of excitement among her students. Of fifty-four students in three different classes, none was able to identify BGH and CEI as equilateral, but they all tried very hard to find them. The second source of excitement came from the handful of students who were eager to know how the solution generalizes to larger arrays.