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    You are here: Home / Learn / Math Activities / Geometry Magic: Turn 2 Circles into 1 Square

     

    Geometry Magic: Turn 2 Circles into 1 Square

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    It's been a while since my son and I made math art magic with Möbius strips and it was time for some more math fun, this time we explored the geometry magic and accomplished the impossible! (Melodramatic, much?)

    Wow your kids with a geometry magic trick.

    We turned two circles into one square.

    "Inconceivable!" you shout. "No one can turn two closed curves into a regular quadrilateral!"

    "Ah, ha!" I answer, "That is this power of math."

    But seriously, this geometry paper trick is totally awesome and you will amaze and impress your children when you show them how it is done. And isn't that our goal in life? (Note: I included affiliate links in this post.)

    What you need:

    • 2 paper strips of equal length. I used origami paper to make it snazzy and pretty.
    • tape
    • scissors
    • a passion for the thrill of math

    Instructions:

    (To see the trick in action watch the video below.)

    Form one strip into a circle. Tape.

    Loop the second strip through the circle in the manner of a paper chain. Tape.

    Securely tape the two circles together. Important: tape loops together on both sides.

    Two loops for a geometry magic trick

    Carefully cut one circle in half lengthwise. Now you have two loops connected by one long strip. (You are correct, this is not a square. Smarty pants.)

    After the second cut of a geometry magic trick.

    Cut the remaining strip down the middle.

    Oooooo, ahhhhhh and say, "Wow!"

    Resulting square in geometry magic trick.

    Watch the magic and be impressed again and again:

    Be sure to pin and share this post, so all your friends can be amazed at how nerdy you are.

    More fun math and paper tricks: 

    • Turn two Möbius strips into interlocking hearts. 
    • Solve the T Puzzle.
    • Try an impossible paper puzzle

    We love math art and math magic so much! It helps my left brain sons get creative and exercise those right brain skills. Discover more terrifically awesome math magic right here:

    Math art projects

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    « Campfire Coloring Page (And a Surprise Conversation)
    Sanity Saving Indoor Magnet Game »
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    Reader Interactions

    Comments

    1. Michelle says

      June 17, 2015 at 5:03 pm

      Oh my gosh, that is hilarious and awesome. 🙂 And you're right, math IS magic.

      Reply
    2. curtasian says

      June 22, 2015 at 12:49 pm

      This was fun to watch but how does math play into it?

      Reply
      • Erica MomandKiddo says

        June 22, 2015 at 1:33 pm

        Topology is a branch of math that is the study of surfaces and shapes.

        Reply
    3. Benjamin Stephen Joseph says

      June 23, 2015 at 11:52 am

      I like circle game please send me more new thanks

      Reply
    4. Karen Murphy says

      June 23, 2015 at 9:04 pm

      Thank you for the fun turning 2 circles into a square post - it saved my afternoon with my 3 grandkids ages 8 and 5. They enjoyed the video, watching it 3 times, and doing the cutting and taping and more cutting gave us something to do together on a rainy afternoon. This activity led to cutting out food for a pretend restaurant, making paper trays to carry the food, etc. It was a great stepping off activity that led to some imaginative play.

      Reply
      • Erica MomandKiddo says

        June 26, 2015 at 10:23 am

        That's wonderful! Thank you for telling me!

        Reply
    5. Anjana says

      July 17, 2016 at 3:42 am

      These are wonderful activities with learning and exploring with fun.
      were awesome?
      Please keep sharing more videos.
      Thankyou.

      Reply
    6. Nisak says

      May 28, 2017 at 8:35 am

      I love it! Its really magic! Turning 2 circles into a square!

      Reply
    7. X says

      February 20, 2023 at 12:04 am

      This was entertaining, but you do realize that you don’t have “2 circles”. You have 2 cylinders. You’re essentially making the strips necessary to make a square. Without restrictions there are other less convoluted ways to achieve the same result.

      Reply

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