Rahul M.
asked • 12/14/20I am looking to split a square into 4 equal areas, not necessarily needing to be the same shapes or sizes . I need to find a way to use the least length of lines ( which could be straight or curved lines) inside the square to split and divide it up. What would be the optimal solution.
Michael M. answered • 12/14/20
Math, Chem, Physics, Tutoring with Michael ("800" SAT math)
This is interesting. I would say if you have a square with area 1, I would cut out two quadrants (quarter circles) in opposite corners each with area 1/4 and then the last cut would be a diagonal from the middle of one quadrant to the middle of the other. This is all just speculation though.
Do the lines need to stay within the boundaries of the square? The smallest number of separate, internal segments that can divide a square into four equal parts is two. Either vertical and horizontal, or from corner to corner.
If you can go outside the square, either one of these solutions could be drawn with one line drawn through the square, then around, then through the square again.
Cool question!
Rahul M.
So basically we have a square of side length 1. I want to divide it into 4 equal areas and they can be any shapes inside it as long as they have the same area. There are restrictions and it must be divided internally. I am not looking for the number of line segments. I am more interested in the total lengths of the lines used to divide the square. I want to minimise this as much as possible. I can do this by using straight lines as well as curves. Could you help clarify this question.12/14/20
Liz Z.
12/14/20
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Rahul M.
Could you please give me a definite answer ? So basically we have a square of side length 1. I want to divide it into 4 equal areas and they can be any shapes inside it as long as they have the same area. There are restrictions and it must be divided internally. I am not looking for the number of line segments. I am more interested in the total lengths of the lines used to divide the square. I want to minimise this as much as possible. I can do this by using straight lines as well as curves. Could you help clarify this question.12/14/20