Enlace Cube Puzzle

My brother gave me this other puzzle (see the previous one here):

Which is the longest line?

I assume this is a square box.

To make things simpler, without loss of generality, let this be a unit box, that is, let its side have length one.

Observe how the lines take circular segment shapes on the faces of the box. So, the lines can be described in terms of a sum of quarter circles. Mathematically, $$ L=\frac\pi2\sum_{i=1}^{n}1=\frac{n\pi}2. $$ In other words, we don't even have to do any math at all; all we have to do is count the number of quarter circles and whichever line has the most is the longest one.

To me, it looks like the blue line has $8$ quarter circles while the red one has $7$. So, the blue line is the longest line.

By the way, bro:

Mi hermano, han pasado tantas cosas este año que tendría que sentarme contigo por un día entero para poder contarte más o menos cómo me ha estado yendo. Ahorita la universidad me está medio matando con exámenes finales, pero tengo planeado escribirte cuando los termine la próxima semana (¡esta vez sí!). :)

No comments:

Powered by Blogger.