Square Within a Square
Nicole Mosteller
EMAT 6690
Which of the solutions
a = 4w or a = w give us the equation for the line
that we desire?
Upon investigation of a = 4w,
we find that the equation for our line would be
and this equation would have the graph
of
Apparently, a = 4w is just an extraneous
solution.
Using a =
w, we find y
= 0 and b
=-2.
After substituting these values as
well as a = c = z,
we find that an equation for our relationship,
results in the desired graph below.
Conclusions:
The investigations made from the Square
within a Square problems use ideas that are fundamental
to the curricula most Geometry, Algebra
II, and Calculus classes. With modifications, this investigations
can be adapted to pose an interesting
and challenging problem for students.
Resources: Thank you to Dr. Red Alford (UGA Math) and
Keith Leatham (UGA Math Ed) additional insights.
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