Garnet SmithAri LibermanSaige RasmussenPre-noteThe entity who
wrote this write up had to sound in third person so that all
parties who worked on the problem go credit. The parties involved
are the ones written above.ProblemThe problem we faced was finding
a pattern to describe and find the maximum amount of pieces one
could cut out of a pie using any amount of cuts. First we were
given the task of drawing out pies with 4 or 5 cuts in them, in
different patterns trying to find the maximum amount of pieces from
4 and 5 cuts. After that we attempted to find a pattern within a in
and out table to accurately describe what was happening. Then we
used the pattern we created to find the amount of pieces you can
get from ten cuts. After that we made a formula or equation with
variables that you can you use to find any amount of cuts and the
pieces outcome. ProcessWe first started by drawing circles and
putting lines through them with a ruler randomly. We then started
to realize that it's more efficient and creates more pieces of pie
if you create close together lines that cross over each other and
after that made lines that crossed over those close together lines.
It made it so it created quite a few pieces and then crossed over
and doubled the pieces or more! We did this 5 times for 4 and 5
cuts and found the maximum amount of cuts for both. We then
imported maximums for 0,4 and 5 to a table already containing
maximum cuts for 1,2 and 3. Then we perfected our rule and made a
equation/formula. SolutionWe examined the table for along time. We
found that when you added 1 to each amount that you added going up
from pieces you got the correct amount of cuts. But this did not
work after 5 which meant it was wrong. We then perfected it and
found that if your looking at the amount of cuts you can find the
amount of pieces. We found that for finding any amount of pieces
all you had to do was take the next number of cuts after your your
desired cuts, and add all number below that except the desired cut
number, but including 0. For instance if your trying to find the
amount of pieces for 4 cuts. Then you would add the next number (in
this instance 5) to all the rest of the number under your desired
cuts (4.) So it would look like this 5+3+2+1+0 which equals 11
pieces. This works for any pieces you want to find from cuts. We
found that the maximum number of pieces from 10 cuts of 56 pieces
when using our method. In this instance for 10 cuts, its
11+9+8+7+6+5+4+3+2+1=56 pieces. To create a formula with variables
we came up with (x+1)+(x-1)+(x-2)+(x+3)+(x-4)...... to the amount
of pieces you're using for x variable. EvaluationWe thought this
POW was a more fun but challenging one. Our thinking for this is
that first we got to play around with cutting pies, and then we had
to critically think, discuss and evaluate different methods of
finding the correct answer. Which took time considering variables.
But we all thought it was quite beneficial working in this group as
we all were able to expand upon each other ideas and formulas to
create a consensus. We think it's a very valuable skill to learn of
having little direction and attempting to find a large formula.
Overall we enjoyed this POW and wish for more like it!
