Bianca Carr
Parris Owens
A’lana Baldwin
Sherrell Haney
Madeline Darbyshire
Group 5
MAT 2120 Project Exercise
Suppose that circles of equal diameter are packed tightly in
n
rows inside an equilateral
triangle. (See the figure below, where the case
is shown.) Let
be the picture showing
the
n
rows of circles and let
be the total area occupied by the
n
rows of circles.
(a) Show
(b) Now compute
..
(c) Determine a general formula for
.
(d) What is
(e) Explain the significance of the result in part (d). For instance, how much of the area
of the triangle will the rows of circles eventually occupy, to the nearest percent, as

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(a)
Show
𝑃
1
, 𝑃
2
, 𝑎?? 𝑃
3
,
and then compute
𝐴
1
, 𝐴
2
,
and
𝐴
3
.
A2: