n-body problems are interesting and challenging. By using the laws of gravitation and a computer and some very clever symmetry, many beautiful (and in a perfect world, stable) orbits are possible!
This set of simulations is one of the most amazing and beautiful I have ever seen. Toggle the trajectories, particularly on the last two in the list.
http://www.maths.manchester.ac.uk/~jm/Choreographies/
Biofabric is a creative way to re-imagine network diagrams. What is particularly impressive is the short animation going from the old view to the new. See the blog detailing the process here.
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Visualizing sports stats is a great way to engage students with the study of mathematics! Here are some of my favorites.
http://statmilk.com/NFL/0/? and http://www.statmilk.com/NCAAF/0/? let you visualize just about anything you would want to know about the NFL and NCAA.
http://www.chartball.com/football/ offers a creative and interesting way to visualize football games.
I hope you enjoy these and are able to work them into your classes. I imagine that many interesting discussions can arise from having students explore statistics with the help of these websites.
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Thank you for sharing your thoughts.