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The AMATYC Review Spring 2006, Vol.27, No.2 |
Building Buildings with Triangular Numbers David L. Pagni |
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David L. Pagni is a mathematics professor at California State University, Fullerton. His interests range across the spectrum of mathematics education from grades K-16. His teaching fields include mathematics, mathematics learning, teaching, and technology. He is currently principal investigator of a National Science Foundation Mathematics and Science Partnership called Teachers Assisting Students to Excel in Learning Mathematics (TASEL-M). E-mail: dpagni@Exchange.fullerton.edu |
| Triangular numbers are used to unravel a
new sequence of natural numbers here-to-fore not appearing on the
Encyclopedia of Integer Sequences website. Insight is provided on
the construction of the sequence using “buildings” as
a viewable model of the sequence entries. A step-by-step analysis of the sequence pattern reveals a method for generating the function. Graphing calculator programs are provided for generating the sequence both recursively and explicitly for different initial “building” sizes. Finally, an explicit formula for the sequence that makes use of the “ceiling” function generalizes the results. |
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