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This Lesson (Forming a rectangle from a square by using dissection) was created by by math_helper(2461)
  About math_helper: MSEE, who has a strong interest in helping others understand concepts related to mathematics.
Here is a problem that was asked recently. Given a square of material, how can one cut that square and rearrange the pieces to make a rectangle? The rectangle shall have length equal to three times the width, and ideally uses all of the material from the square.
I was initially lost on this problem. I found a resource on the web that showed how to make a square from a rectangle and adapted the reverse of that procedure. However, I had failed to realize it was only for rectangles where length is less than twice the width, and we wanted a rectangle where length was three times the width. I continued to research this problem as it seemed so foreign to me: cutting something and re-arranging it does not seem to fit the normal "transformation" where one draws a shape and morphs it into another on paper. It turns out, for rectangles up to l < 4w, you can use the following procedure. I adapted the solution from http://mathafou.free.fr/pbg_en/sol110.html where they go from a rectangle to a square. — — Cut along the lines and rearrange as shown below — — This lesson has been accessed 1999 times. |
