Thursday 23 January 2014

A Geometric "Love" Story - How to draw hearts with circles

Yep, I am going to be one of THOSE people who start celebrating Valentine's Day in January. Here is a special V-Day production I made for both art and math lovers! Aristotle once said, "There is nothing strange in the circle being the origin of any and every marvel." So naturally, the magic of circles inspired the creation of 3 different hearts, the synonym of love.

In Act One, the method is called "curve stitching". Each tangent line segment moves around the circle and eventually envelops the shape of a heart. Act Two draws what I call a chubby, smiley heart, the cardioid. It is formed by evolving circles centring on and passing through the same point on another circle. And lastly, each heart is formed by the partial outline of 4 circles. Simple and sweet! All you have to do is shift your perspective to see it. This post also shows many, many other ways to draw a heart using mathematical concepts. Check it out and maybe you will find some cool ideas!

I also manage to sneak in three other quotes that I thought went really well with the scenes!

To make the knitted heart shown in Act One, you will only need a cork board, 72 pins, and some pretty yarn or string. 
First, follow the method shown in video and use below template as a guide to evenly place 72 pins in a circle. A longer string will make a bigger circle, and vice versa. Remember to pull the string taut over each dot.  
Next, follow the process shown in video and wrap the string around the pins (nodes) according to the following 10 templates. "Set 1: Start Nodes 0-15 (every +1), End Nodes 15-30 (every +1)" means: 
  1. You start from Node 0 and bring your string over to (end at) Node 15. 
  2. Wrap around Node 15 and bring string back to Node 0.
  3. You move starting node by one (15+1=16) and ending node by one (0+1=1) 
  4. Repeat Step 1-3 for Node 1 and Node 16.
  5. Repeat until you finish Node 15 to Node 30, then continue onto the next set. 

Set 1: Start Nodes 0-15 (every +1), End Nodes 15-30 (every +1)

Set 2: Start Nodes 16-20 (every +1), End Nodes 32-40 (every +2)

Set 3: Start Nodes 21-26 (every +1), End Nodes 43-58 (every +3)

Set 4: Start Nodes 27-29 (every +1), End Nodes 60-64 (every +2)

Set 5: Start Nodes 30-36 (every +1), End Nodes 66-72 (every +1)

Set 6: Start Nodes 72-57 (every -1), End Nodes 57-42 (every -1)

Set 7: Start Nodes 56-52 (every -1), End Nodes 40-32 (every -2)

Set 8: Start Nodes 51-46 (every -1), End Nodes 29-14 (every -3)

Set 9: Start Nodes 45-43 (every -1), End Nodes 12-8 (every -2)

Set 10: Start Nodes 42-36 (every -1), End Nodes 6-0 (every -1)

Happy Valentine's Day!


  1. I love this post! Thank you so much for giving a beautiful art project to math teachers! Where can I find the instructions for making the cardiod?

  2. Here is one: :)