Defending The Perimeter

Larkin and Finn recently watched some math lessons, cleverly disguised as the PBS cartoon CyberChase. They were *really* fascinated by the distinction between perimeter and area and were immediately inspired to break out the ol' blocks.

They counted out 9 square blocks to play with and it didn't take long for them to figure out that the optimum configuration for minimum perimeter with their fixed number of blocks was a square:

They quickly made the leap to maximum perimeter being a straight line:

I then totally blew their math-addled minds by claiming that the perimeter of a stair-case was the same as the line:

They both predicted, quite definitively, that the staircase would have a perimeter somewhere between the minimum and maximum and were shocked (shocked, I tell you!) when they counted the edges to reveal that my claim was true. I was declared a Math Fiend when I convinced them that perimeter was determined solely by the number of shared sides so they could make any crazy pattern as long as they kept that constant. This was proven, rather exhaustively, by construction.