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  • Square Puzzle
    cool stuff/square puzzle/

    Let's say that you have a square-shaped garden and you want to double the size of your land. The government, however, forbids you to have a garden that's any shape other than a square. How would you do this?


    Figure 1
    Doubling the square land seems easy. Since each side of the square is, let's say, 2 metres long, you try doubling the length of each side. Uh-oh! You will end up with a square four times as large as the original one!
    Figure 2
    You try dividing your square land into four small squares. Next, you add on four new squares the same size as the small ones. This way, you would have twice the amount of land. Wrong! You would end up with a rectangle, not a square!
    Figure 3
    You try adding two small squares to one side of the original square and two to another side. You realize that you end up with a square with a part missing. If you were to fill in the missing part, you would have a garden that is more than double the size of the original square.
    Figure 4
    Again, you try to look for another solution. You try dividing the original square into four parts by drawing diagonal lines between the opposing corners. Maybe, if you could add four more triangles of the exact same size, you might be able to make the double-size square!
    Figure 5Figure 6Figure 7
    It turned out to be a diamond first... But when you turn it diagonally... It's a SQUARE!!!
    And that's how you double the size of a square and still end up with a square!

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