MA-351 Homework 4
Tuesday, Nov 14, 10:15am, in class.
Solutions may be submitted in person in class,
or you may email an ASCII text,
Maple Worksheet (.mws),
html, or postscipt/pdf-formatted document to me
(kaltofen@math.ncsu.edu).
Note my office hours on my
schedule.
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Please consider the formula
a-b*c/(d+f)+g
Please give the parse tree for this expression
according to the context free grammar for expressions given in class.
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Please consider the following variant to Fibonacci's rabbits' problem.
Each pair of rabbits takes two months to mature.
Once mature, the pair has one or two pairs of rabbits after every month
of gestation. Therefore, it takes a newly born pair 3 months
to produce offspring. The number of pairs is produced
alternatingly: first one pair, then two pairs then one pair, then two pairs, etc.
Please give a Lindenmayer system that models the growth
and show the first 6 generations of applying your rules.
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Consider a fractal called the Sierpinski gasket. You start with
an equilateral triangle. Remove the equilateral triangle formed
by the midpoints of the three edges. This leaves 3 equilateral
triangles of the same size at the corners. Recur the procedure
with these triangles.
Compute the remaining area (drawn in black in the above
picture) as a fraction of
the area of the original triangle when this procedure is continued to
infinity.
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DMM §3.6, Problem 13, page 168.
Note that your coloring also needs to include the
country "11" surrounding countries 1-10.