id: 06664469
dt: j
an: 2016f.01192
au: Gilbertson, Nicholas J.
ti: Integer solutions of binomial coefficients.
so: Math. Teach. (Reston) 109, No. 6, 472-475 (2016).
py: 2016
pu: National Council of Teachers of Mathematics (NCTM), Reston, VA
la: EN
cc: K20 F60
ut: binomial coefficients; integer solutions
ci:
li: http://www.nctm.org/Publications/Mathematics-Teacher/2016/Vol109/Issue6/Integer-Solutions-of-Binomial-Coefficients/
ab: Summary: A good formula is like a good story, rich in description, powerful
in communication, and eye-opening to readers. The formula presented in
this article for determining the coefficients of the binomial expansion
of $(x+y)^n$ is one such “good read.” The beauty of this formula is
in its simplicity ‒ both describing a quantitative situation
concisely and applying it with straightforward calculations. Delving
deeper, however, reveals countless interesting connections, patterns
(e.g., Pascal’s triangle), and applications. What is particularly
important about the two approaches presented here is that they are very
different and yet they end up in the same place. Attending to what the
situation represents (i.e., combinations) provides insights different
from those that arise when we focus on the structure of the formula.
Although the proof may be more complicated than many students can
handle, the main ideas are still accessible. (ERIC)
rv: