The Beauty of Symmetry: An Introduction to the Wallpaper Group
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Resources used in the video:
Web app to generate all 17 wallpapers: https://math.hws.edu/eck/js/symmetry/...
Lots of images for each element of the wallpaper group: https://en.wikipedia.org/wiki/Wallpap...
The aperiodic monotile: https://cs.uwaterloo.ca/~csk/hat/
There are precisely 17 different periodic tilings of the plane. That is, demanding translational symmetries, we can investigate the possible rotational, mirror reflection and glide reflection symmetries and it creates the so called Wallpaper group with 17 possibilities.
0:00 The wallpapers of Alhambra
1:07 The four symmetries
2:31 The symmetries of pmg
5:55 Tilings and lattices
8:02 the 17 wallpapers
10:20 The symmetries of p6
12:45 The symmetries of cm
13:50 Plotting all 17 wallpapers
14:28 Why only rotations of 2,3,4,6
17:02 New research on aperiodic tilings
17:50 brilliant.org/TreforBazett
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