Make Valentine’s Day crafts to celebrate loving one another… in the context of mathematics!

Grow your math eyes on these little field trips inspired by topology, dynamical systems, and algebraic geometry for the young, the very young, and the young at heart.

Know another romantic math craft? Tell us in the comments!

**Make math:** Fold paper in two. Sketch a teardrop in such a way that the fold forms one side of its triangular top part. Cut it out, open, and decorate the heart-shaped greeting card. My teen and I decorated with a cardioid (see below).

**Grow your math eyes:** What interesting shapes can you fold or unfold into other interesting shapes? What if you fold more than once? Choose shapes to experiment, on paper or in your imagination.

**Topic:** Mirror Symmetry. **Inspired by Big Math:** #14 Algebraic Geometry, #53 Differential Geometry.

**Bonus:**

**Make math:** Cut out two strips of paper and glue them together to form the + sign. Attach the opposite ends, with a twist, as if making Mobius strips. Cut the strips through the middle, and Mobius Hearts will happen! Video instructions:

**Grow your math eyes:** Try twisting two or more times. Try cutting 2/3 of the way rather than through the middle. What other surfaces can you make by connecting, twisting, and cutting paper strips?

**Topic:** Surfaces. **Inspired by Big Math:** #54 General Topology, #57 Manifolds.

**Bonus:**

*Roses are red. Violets are approximately blue.*

* A paracompact manifold with a Lorentzian metric,*

* can be a spacetime, if it has dimension greater than or equal to two.*

By Sarah Kavassalis

From participants in the Multiplication Explorers course

**Make math: **Draw a heart. Mark two or more points around it, for example, up top. Draw smaller hearts there. Mark the same points on them, and draw even smaller hearts. Keep going. Decorate your heart fractal, put it on a wall, or use as a greeting card.

**Grow your math eyes: **How tiny can your hearts become? Will you run out of space on paper if you keep going and going and going? How many hearts do you add to your fractal at each step of the process? For more versions, choose how many hearts to add at each step, how much to shrink at each step, how to turn the hearts around – then observe what happens.

**Topics:** Fractals and exponential growth. **Inspired by Big Math:** #11 Number Theory, #37 Dynamical Systems.

**Bonus:**

**Make math:** Trace a plate on scratch paper and cut out the circle. Fold it in half a few times, as if for making a snowflake. Unfold; your circle is now split into equal parts.

Trace the same plate on cardboard. Then use your folded circle as a guide to mark your new circle. You may need to insert more dots by hand.

Image by Cory Poole/WonderHowTo

You can also print out a marked circle, or use a protractor to mark it. Then follow instructions from MathCraft for drawing, or Almost Unschooling for string art. The craft involves skipping the dots by one and two, again and again. The repetition feels meditative, and there is a beautiful surprise at the end. The heart-shaped curve emerges as if by magic! Decorate it and put it on the wall or use as a greeting card.

**Grow your math eyes:** What other curves can you make out of straight lines? Choose your own “recipe” for skipping dots around a circle, and see what happens. What if you used a triangle or a square instead?

**Topic:** Curves. **Inspired by Big Math:** #14 Algebraic Geometry, #52 Discrete Geometry.

**Bonus:**

**Make math: **Customize variables and make your own greeting cards out of pretty graphs. Go to **Desmos Math-o-Gram site** to play and share the love.

**Grow your math eyes:** Peek behind the scenes to experiment with the equations. Replace numbers or functions in them and see what happens. Young children can start experimenting without knowing much (or anything) about the functions.

**Topic:** Functions and graphs. **Inspired by Big Math:** #14 Algebraic Geometry, #33 Special Functions.

**Bonus:**

The heart Earth theory from Wolfram Alpha.

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