Monday’s Problem
October 9th, 2006 by SplineGuy
I thought I’d throw out a simple little problem that intrigued me and led me off on a wild goose chase. In the end, I got almost none of my intended work done before class, while I was exploring all sorts of problems of perimeters of overlapping figures.
PROBLEM:
Pairs of identical rectanglular strips, each measuring 3 by 1, are overlapped in a number of different ways to form three different shapes, shown in the diagram below.
Which shape has the greatest perimeter?
I accept that this is really not that difficult of a problem but the question that got me distracted was the last of the following: What if the dimensions of the rectangles were 5 by 2? 9 by 7? a by b?
What if the rectangles do not overlap at right angles?
Being a completely non-mathematical person, but wanting to venture a qucik guess … just by looking at the diagrams, shouldn’t all three have the same perimeter, or have I just embarrassed myself by suggesting such a thing?