Valentine’s Day Maths – Linked Möbius Hearts

Are you looking for a Valentine’s Day gift for someone who loves maths?

Then look no further as we have instructions on how to make a pair of Möbius hearts which not only look great but also have mathematical significance – surely making them even more special for the one you love!

Step 1

Take two strips of paper which are the same length and width (in red or pink if you are heading for a traditional Valentine’s Day theme).

Step 2

Stick these two strips of paper together at right angles in the middle to form a cross shape.  You can use glue or sellotape – however sellotape might be more sturdy.

Step 3

Take one of the strips, give it a twist and then stick the two ends together.

Step 4

Take the other strip, give it a twist and then stick the two ends together.  Important: If you gave the first strip a twist to the right, then make sure you give this strip a twist the opposite way, to the left.  You should now have two Möbius strips which are stuck together at right angles.

Step 5

Carefully cut down the centre line of both of the two loops, all the way around.  Gently spread out and untangle what you have made, until you have two interlinked Möbius hearts.  At this point you may wish to make further reinforcements with glue or sellotape.

What if it hasn’t worked?

If you have not created two interlinked hearts, you have probably given both your original Mobius strips a twist in the same direction, instead of in opposite directions.  This means your creation will not have worked.

What is the mathematical (and romantic) significance of my two Möbius hearts?

A Möbius strip is a special mathematical shape which only has one side.  In terms of romantic significance a one-sided shape is surely pretty special and could stand for the unity or one-ness of a couple, or any other romantic comparison which you might care to make.

Unfortunately the individual hearts which you have created are not in themselves Möbius strips.  However it is still pretty cool that they were made out of two Möbius strips.

Read more about the amazing mathematical properties of a Mobius strip here.

Mobius Strip Video

Take a look at this Numberphile video which not only shows how to make Möbius hearts but also explores what happens when you repeat the instructions above with other options such as a straight loop and Möbius strip stuck together.  You will be surprised by the shapes which you end up with!

Article by Hazel Lewis