# Derivation and Visualization of the Binomial Theorem

Derivation and Visualization of the Binomial Theorem The binomial theorem presents us with the opportunity to weave many different mathematical strands into one lesson. It has a fascinating history — the study of which leads to a better understanding of how mathematics evolved. In this paper, we have involved computer graphics, geometry, algebra and combinatorics in the derivation of the binomial theorem. The study of functions with finite domains and ranges helps students understand some of the more subtle properties of functions which have the set of real numbers for their domain and range. These are the functions which they study to the exclusion of all others in high school and in their first two years in college. We believe that the lesson presented in this paper encourages students to express mathematical ideas in the vernacular, one of the major standards recommended by the National Council of Teachers of Mathematics (NCTM). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Technology, Knowledge and Learning" Springer Journals

# Derivation and Visualization of the Binomial Theorem

, Volume 5 (1) – Oct 5, 2004
22 pages

/lp/springer-journals/derivation-and-visualization-of-the-binomial-theorem-TVpzGVTzHx
Publisher
Springer Journals
Subject
Education; Learning and Instruction; Mathematics Education; Educational Technology; Science Education; Creativity and Arts Education
ISSN
2211-1662
eISSN
1573-1766
DOI
10.1023/A:1009873212702
Publisher site
See Article on Publisher Site

### Abstract

The binomial theorem presents us with the opportunity to weave many different mathematical strands into one lesson. It has a fascinating history — the study of which leads to a better understanding of how mathematics evolved. In this paper, we have involved computer graphics, geometry, algebra and combinatorics in the derivation of the binomial theorem. The study of functions with finite domains and ranges helps students understand some of the more subtle properties of functions which have the set of real numbers for their domain and range. These are the functions which they study to the exclusion of all others in high school and in their first two years in college. We believe that the lesson presented in this paper encourages students to express mathematical ideas in the vernacular, one of the major standards recommended by the National Council of Teachers of Mathematics (NCTM).

### Journal

"Technology, Knowledge and Learning"Springer Journals

Published: Oct 5, 2004

### References

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