Spider likes to walk in a shed during the night. It can walk on its floor, walls, ceiling. The shed is a prism. Dimension of shed is a x b x c.
What is the closest way from start to finish?(image)
I think it can be. $$ \sqrt[2]{a^2 + b^2} + c $$ or $$ \sqrt[2]{a^2 + c^2} + b $$ or $$ \sqrt[2]{a^2 + c^2} + a $$
I bet it is the first option, but I do not know how to proove it.
When we unfold the prism, we can get a few nets. For now, we will take the nets with the 4 rectangles lined in a row. That means the top 6 in this picture.
http://en.wikipedia.org/wiki/File:Planificacao_cubo.gif
Without loss of generality, let the side with 'a' on it be on the second rectangle. Using the nets, I will leave you to put the points down and draw the lines.