Boldly Folding (part 1)

Algebra Level 3

You have a rectangular piece of paper of width \(W\) and length \(L\). You pick up the left side and fold it to the right side, like so:

Which function describes the new position of a point \(P = (x, y)\) on the paper after the fold?

  1. \(f(x, y, W, L) = \left\{ \begin{array}{rl} (W-x,y) &\mbox{ if $x<\frac{W}{2}$} \\ (x, y) &\mbox{ otherwise} \end{array} \right.\)

  2. \(f(x, y, W, L) = \left\{ \begin{array}{rl} (W^{2}-x,y+L-W) &\mbox{ if $x>\frac{W}{2}$} \\ (x, y) &\mbox{ otherwise} \end{array} \right.\)

  3. \(f(x, y, W, L) = (W - x, L-y)\)

  4. \(f(x, y, W, L) = (\frac{\pi x}{W}, \frac{y}{\pi L})\)

Details and assumptions:

  • The paper has infinitesimal thickness.
Dragon folded by Satoshi Kamiya.

Problem Loading...

Note Loading...

Set Loading...