Moment of Science: Impossible Science

As you prepare for Discovery Cube Orange County’s Impossible Science LIVE, test your hand at making impossible science…possible.

Here’s our challenge:

Can you take a single sheet of paper and using only one cut turn it into a letter of the alphabet?  Go ahead – try it!

Have you figured out how to do it?  The answer to this seemingly impossible challenge is math.  The “Fold and Cut Theorem” states that we can create any 2-dimensional shape that is made out of straight lines.  The secret is folding the paper so the lines you want to cut all line up on top of each other.

Follow the instructions below to learn how to spell out the word “LIVE”.

L:

  1. First, fold the bottom right corner up and to the left until the right edge matches up with the left edge of your paper.
  1. Next, cut about 2” in from the bottom left corner all the way to the top of the page.
  1. Finally, unfold the paper and you will have the letter “L”. Notice how the short edge and the long edge were both cut using a single cut because the two inside edges of the “L” were on top of each other.

    I:

    1. First, fold the paper in half, width-wise, where the right long edge is now touching the left long edge.
    1. Next, fold the paper in half again, but this time take the bottom edge and fold it upward so it is touching the top edge.
    1. Then take the bottom right corner and fold it up and to the left so that it touches the left edge.
    1. Using your scissors, cut in a straight line about 3” above the bottom left corner of the paper.
    1. Unfold your paper and you will have an “I”. Notice that you lined up the four small cuts that form the inside of the top and bottom of your “I” and the inside long lines of your “I”.

      V:

      1. Start by folding the paper in half, width-wise, where the right long edge is now touching the left long edge.
      1. Then take the top right corner and fold it downward so that it sticks over the left edge of the paper by about 2”.
      1. Cut at an angle about 1” in from the bottom right corner, aiming upward so that your cut finishes at the top point where your paper overlaps.
      1. Unfold your paper and you will have a “V”. Notice how you lined up both the inside edges and the outside edges of the “V” and cut them using only one cut.

        E:

        1. First, fold the paper in half length-wise, so the bottom edge is now touching the top edge.
        1. Once again take the bottom edge of the paper and fold up. This time you want your edge to stop about 1” below the top edge of the paper.
        1. Now take the top right hand corner and fold it down so the right edge is parallel to the bottom edge of the paper, but several inches lower.
        1. Finally, using your scissors, cut about 1” in from the right hand edge of your paper, making sure to cut in a straight line all the way to the top of your paper.
        1. Unfold your paper and you will have an “E”. Notice that you lined up all of the straight lines inside the “E” and cut them using one single cut.

          Once you have mastered the challenge, show your family and friends.  And remember, “When you ask the right question, everything changes.”

          Now that you know to line up all the straight edges, can you figure out how to form different letters?  Can you spell your name? If you need help figuring out the math, visit: http://erikdemaine.org/fonts/simplefoldcut/.