ma017 - n n Looking at k k and 1 k k2 Geometrically 1 Eric...

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Looking at and Geometrically Eric Hegblom The Mathematics Teacher , October 1993, Volume 86, Number 7, pp. 584–587 Mathematics Teacher is a publication of the National Council of Teachers of Mathematics (NCTM). More than 200 books, videos, software, posters, and research reports are available through NCTM’S publication program. Individual members receive a 20% reduction off the list price. For more information on membership in the NCTM, please call or write: NCTM Headquarters Office 1906 Association Drive Reston, Virginia 20191-9988 Phone: (703) 620-9840 Fax: (703) 476-2970 Internet: http://www.nctm.org E-mail: orders@nctm.org Article reprinted with permission from Mathematics Teacher, copyright October 1993 by the National Council of Teachers of Mathematics. All rights reserved. Eric Hegblom is a student at Cornell University majoring in applied engineering physics. He resides at 8 Woodfield Road, Wellesley, MA 02181. T wo commonly taught algebraic sums are The first equation has a short algebraic proof, and the second has a more intricate one. An alternative approach is to evaluate the sums geometrically. A method for each sum is presented here. Evaluating the first sum involves positioning squares and then determining area. Evaluating the second sum involves arranging cubes then determining volume. Although this article can use only two-dimensional pictures to demonstrate the second sum, manipulating (three-dimensional) physical cubes adds considerable clarity to a presentation. To find the first sum, we position the squares with sides of length 1, as shown in figure 1, laying one square on the first row, two squares on the second row, three squares on the third row, and so on up to the n th row, on which we lay n squares. Thus the area of this shape equals the sum 1 1 2 1 3 1 4 1 ??? 1
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ma017 - n n Looking at k k and 1 k k2 Geometrically 1 Eric...

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