Counting Diagonals
by Dan Meyer
skips
questions
Sequel






How many squares would a diagonal through the largest rectangle hit?






How many squares does the diagonal go through? Can I figure out a rule without drawing?





Create a formula that can predict how many squares the diagonal will cross through in any given quadrilateral.



How big is that rectangle? Is there a relation between the size and how many squares the diagonal will intersect?


Is there a general formula that would give me the number of squares I pass for a random rectangle?

How can we minimize of maximize the proportion of squares which are passed through?




Through how many squares does the diagonal of an (m x n) rectangle pass?












How can you predict the number of squares that the diagonal will pass through?



how many squares would a line pass through corner to corner? can we generalize this formula?


Given x and y dimensions of a rectangle, how many boxes will be intersected by the diagonal.


How many squares will it cross? Can you do it by just knowing the length and width of the rectangle? How much does this software cost?


Why does the line for the 10 square touch more subsquares than the others? What will the pattern be for the last area shown?





Can you find a function d(x,y) that predicts how many squares the diagonal will hit for general integers x and y?


How many squares would the diagonal pass through for an M by N rectangle?





i have no idea how many boxes it will cross thru. but i really wanna know! guess i'll give this 2 the kid that always finishes early!





What's the relationships between area and the number of squares a diagonal passes through?




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