Square Partitions
by Dan Meyer
skips
questions
Act One
Act Three
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Sequel
 1.
Currently, the right side is divided at 1/n where n = 2. What happens to the regions if n = 3, 4, or we let n approach infinity?
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If the one side of the square has been split into two equal parts, are two of the angles equal as well?





What % of the total area is in each region?Is there a relationship between location of diagonals and area?



What happened to the numbers? Not where did they go...what did they change to?

At what rate do each of the four percentages change when you move the point?




As the line moves down a side, does the area of the four regions grow/decline proportionally?













Which area changes at the fastest rate as the point on the right moves down. Determine the rate of change for each.




















What are the new percents/areas after the line has been moved down? Cool graphics.









how big is each section? sidenote: this is a highly refined digital question. Creation of these things > online versions of textbooks.








What's the size of each area as a percentage of the size of the square?

How do the areas change as the endpoint of the diagonal moves? (honestly intriguing!)





Is this easier to solve given one of the percentages of the final image?


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