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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.

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HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.


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