The final completion of my 2013 calendar, Graphical Astronomy, has been delayed, so at this point I am going to update the dates for 2014 and post it this fall. As partial compensation, I’ve created a Valentine’s Day card for mathematically-inclined people that can be downloaded, printed and folded. It is appropriate whether the person giving the card or receiving it is interested in math, or both, and in fact it’s not Valentine’s Day specific so it can be used for birthdays or anytime at all.
Using a cardioid to represent a heart is not new, but I re-created the complex construction on the front from an old doctoral dissertation of 1900 by Raymond Clare Archibald at Kaiser-Wilhelms -Universität Strassburg. I plotted the curves in vector form in Mathematica and added the lines and text in Adobe Illustrator. I stylized the cardioid in the center of the figure by plotting several versions of it where I added a small parabolic term to the equation so for each curve the width of the cardioid in the middle varied. The straight lines are gray, actually, so the figure will be less cluttered when printed than when you view it normally in the PDF (you can zoom into the PDF to see this).
The image below provides a low-resolution view of the outside and inside of the card before folding down the middle, although the gray background is not included in the actual PDF. As you can see from the inset picture at the top of this essay, the curves and lines on the front side are much sharper then they appear here. The link downloads the vector-resolution PDF with rotated images that you would print in double-sided Portrait mode to line up the outer and inner images correctly for a side-opening card. Of course, it looks best on photo paper or glossy color cardstock, and perhaps at a bit smaller size than 8.5″x11″. It should scale appropriately for A4 or other paper sizes. You will probably want to write the event on the front and write something on the inside.
There is no indication on the card of its origin. If you ever want to know where you downloaded it from, you can find my contact information in the PDF file under the File—>Properties menu option of Adobe Acrobat. And if you would like something different printed inside or on the front, just write me using the Contact Me link in the lower right side panel of this blog and I’ll be happy to customize it for you.
P.S. I stumbled across a nice image for a music-themed Valentine’s Day card: The sheet music of Baude Cordier (c. 1380-1440) titled Belle, Bonne, Sage (Beautiful, Good, Wise). Have a look! According to Wikipedia, the red notes in this love song indicate rhythmic variations.