Fun With One Cut

Inspired by a brilliant talk by Erik Demaine, I started playing around with the famous one-cut problem:  given a shape made up of straight line segments, can you fold the paper flat in such a way that with only one straight cut your shape will appear?

Having no real experience with mathematical paper folding, I thought I’d try out a Koch Curve.  Well, a finite iteration of it, at least.

Koch 1

It seemed like the strategy was to use the symmetry of the shape to make all the line segments line up on each other.  So I folded down the middle, and then again down the new middle.

One-Cut Collage 1

 

I rotated the last shape and it seemed a little clearer how to continue.

One-Cut Collage 2

It seemed like all the lines were lined up, so to speak.  So I cut.  And voila!

Koch 2

Not too bad!  Now, if I could just figure out how to do this with non-symmetric figures.

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Rock, Paper, Scissors

NYT rock paper scissorsThis is a great interactive Rock-Paper-Scissors game from the New York Times website:

http://www.nytimes.com/interactive/science/rock-paper-scissors.html

The computer will narrate its strategy for you as you play, telling you whether it has correctly predicted your choice or not.

Skeptical?  Play the game against the Veteran computer and watch it beat you!  Then, go check out this infographic for some tips on how to improve your play.

It might be fun to pit a 6-sided die against the computer to see what happens.

Math Quiz: NYT Learning Network

Gold barThrough Math for America, I am part of an on-going collaboration with the New York Times Learning Network.  My latest contribution, a Test Yourself quiz-question, can be found here:

http://learning.blogs.nytimes.com/2011/03/02/test-yourself-march-2-2011/

This problem is based on the re-opening of long-closed gold mines due to the rising price of gold.  Apparently, it’s now financially worthwhile to go back in and collect the scraps that were left behind.

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