Valentine’s Day Math


mobius-heart-5.jpgLooking for a last minute homemade gift for a loved one on Valentine’s Day? Make a set of interlocking Möbius Strip Hearts! All that’s required is paper (enough for two strips), tape or glue, and scissors.

To begin, cut out two strips of paper. Make each one into a Möbius Strip, twisting in opposite directions (right and left, or clockwise and counterclockwise). [This twisting in opposite directions turns out to be a crucial design element, as I discovered the first two times I made this: otherwise, the hearts are disconnected at the very end and don’t even look like hearts. It’s really sad.]


Now glue or tape the two Möbius strips together so that they are perpendicular to each other where they meet. (I joined them at the seam of each Möbius strip so that the seams would be less visible in the final product.)


Cut the two strips lengthwise, as illustrated by TwoPi. This will mean that the overlapping square where they are joined will get quartered. If you’re doing this with kids, then you can draw a line down the center of each strip of paper (both sides) before creating the Möbius strips, and that will help guide the cutting.


When you’re done, you’ll have two interlocking hearts! They’re a little bit twisted, but hey, aren’t we all?


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16 Responses to “Valentine’s Day Math”

  1. Jackie Says:

    What a great idea, thanks!

  2. Rich Says:

    each strip of paper (both sides)

    BOTH sides? I’m having trouble finding the second side!

  3. Ξ Says:

    Indeed — if you draw the line AFTER creating the Möbius strip then you’ll only need to draw a line on one side (but the line will be twice as long). If you draw the line while they’re still strips of paper — which is a little easier — you’ll still have two sides per strip.

    (Doesn’t that make Möbius strips sound like a weight-loss type ad for strips of paper? “With our special half-twist, you can reduce your number of sides by 50%!”)

  4. Sheryl Says:

    Great idea, I had seen before on a math site though like the graphics you have used. I would like to share this with parents/kids as a way to show linkage in their hearts (all year long). Could I have your permission to use in a pamplet I am writing? Combination of acupuncture energy points, and familiar things for people to do to keep their mind, body and spirit integrated.
    thanks for your consideration.

  5. Ξ Says:

    Sheryl, thanks! I’m happy to give permission for you to use the images (and would love to see a pamphlet when you’re done if that’s convenient) — thanks for asking! I have larger versions of the photos (these were resized before posting) if those would be better/clearer for the pamphlet.

    (I’ll send you an email as well — my email is “hlewis5” and “” with the @ sign between those two parts.)

  6. A Pop-Up Sierpinski Valentine Card « 360 Says:

    […] Pop-Up Sierpinski Valentine Card By Ξ Last year we made interlocking Möbius Valentines.  This year we’re going staying three-dimensional, and making a pop-up card that forms a […]

  7. Breaking the boundary « West Coast Swing blog Says:

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  8. Valentine chemistry « Henry Rzepa Says:

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  12. Valentine’s Day, send Mobius Hearts our Way! « Number Loving Says:

    […] of mobius strips to pupils, finishing the lesson of with these fantastic mobius hearts. The 360blog here gives a step by step guide to making your mobius hearts. Take a good look round 360′s blog […]

  13. The Sierpinski Valentine, Cardioids, and Möbius Hearts « Math Munch Says:

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