Projective Geometry

For Christmas of 2012, my family and I travelled to see my folks and my sister. As a gift, I brought along Spot-it! by Blue-Orange Games, which Amazon had suggested I might like. It was spot-on! I spent the holidays playing with this game, fascinated that each pair of cards contained exactly one symbol in common. There were 8 symbols per card. I could see how one could accomplish this for 49 cards, but I could not figure out how this could be done with 55 cards, and this started my internet searching and my interest in this puzzle. It turns out that this can be done for up to 57 cards, and my goal became to arrange the scrambled set of cards into an easily verfiyable arrangement so that one could visually verify the underlying projective and affine planes in the system. After a few weeks of tinkering with it on and off, my mission was accomplished. Michael suggested I write down my ideas, and now have a paper accepted for publication in "Eureka", a journal which originates from the undergraduates at Cambridge University. I wrote a javascript app for the n=3 game and another one for the n=5 game. I used both of these in my MATH 154 course at American University.
link to Projective Geometry 3 app link to Projective Geometry 5 app

Here are videos on youtube of me explaining my projective geometry
apps and associated concepts for my students who were reviewing for
their final.

Here is a preprint of the paper and a copy of the slides from the talk I gave at MOMATH in August of 2013 on this topic.

Flipping corners Rotating corners