Friday math movie: Using slope to bust a magic trick

By Murray Bourne, 13 Jan 2012

You've probably seen this famous puzzle.

8x8 square becomes 5x13

On the left is a square with sides 8 units. This gives us 64 small squares. After cutting the square into 4 pieces as shown, we can re-arrange them to give a rectangle with dimensions 13 × 5 units. This gives us 65 small squares.

Where did the extra square come from?

Try to solve it before watching the video!

This week's movie gives us some insight into this problem.

Video by: Math Pickle.

See the 3 Comments below.

3 Comments on “Friday math movie: Using slope to bust a magic trick”

  1. Carlos says:


    My name is Carlos Rodriguez and I wanted to introduce myself and my product to you, since it might be of interest to a fellow student of geometry. My invention is the Versa Ruler, the world’s first shape-making ruler. It’s a connectable system of rulers and protractors capable of forming and locking an unlimited number of 2-D rectilinear shapes. Please take a look at our video, and I would welcome any comments.

    Video: Shape-making Versa Ruler

    Thank you–

    Carlos Rodriguez

  2. Murray says:

    @Carlos: Thanks for alerting me to your interesting ruler. I found this part interesting on your page:

    With so many of our tactile experiences going digital, our mission is to nurture both creativity and productivity at a visceral level. And as our education becomes more visual, the honing of our aesthetic senses will play an increasingly vital role in how well we learn.

    All the best with your venture!

  3. Carlos says:

    Thanks Murray. Aesthetics is a philosophy that is sorely under-taught in our education system. Adaptability is another. For those who seek it, I really do believe that there's a new renaissance of ideas, art, and technology on the horizon. One that is being brought about by the confluence of minds that is the internet. Anything that you want to learn is available instantly at your fingertips. Simply amazing...

    Great talk and great blog. Take care!

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