Boldly Folding (part 1)

Algebra Level 3

You have a rectangular piece of paper of width W W and length L 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 ) 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 ) f(x, y, W, L) = (W - x, L-y)

  4. f ( x , y , W , L ) = ( π x W , y π L ) 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 .
4 1 2 3

Brock Brown by Brock Brown , 25, USA

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1 solution

Brock Brown
Jul 7, 2015

First of all, we know that all y y properties will be the same after the fold. How will x x change?

We want to mirror our left side over to the right with the following transformation:

f ( x , y , W , L ) = ( W − x , y ) f(x, y, W, L) = (W - x, y)

In order for this function to be applicable to all points on the paper, we need to add a part that says the transformation is restricted only to the left side:

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.

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