Also there’s definitely something going on with these stained glass windows in Mainz cathedral. What do you notice? What do you wonder? #NoticeWonder
Better view of the blue squares pattern here: https://www.flickr.com/photos/hans_r_van_der_woude/33336621330/
I don't know who needs to hear this, but the term "woke" didn't start with kids on Twitter.
The was first recorded by Lead Belly in the 1930s in a song called "The Scottsboro Boys," about the dangers Black Americans faced traveling through states in the Deep South. The original line was "best stay woke," as in, "remain aware of the dangers of racism."
Black communities shortened the term to "stay woke," over time, and eventually added "woke" as a state of being--or constant awareness.
I modified my 3D-printable spectre montile so they fit together easily. This single tile tiles the plane aperiodically and only aperiodically. It is obtained from the polygonal tile by adding or removing semicircles on each unit-length edge.
Download: https://www.thingiverse.com/thing:6053252
More info: https://arxiv.org/abs/2305.17743
This 3d-printable tile is based on the one discovered by David Smith, Joseph Samuel Meyers, Craig S. Kaplan, and Chaim Goodman-Strauss in May 2023 (see: https://arxiv.org/abs/2305.17743). It is an example of an "einstein"—a single shape that tiles the plane aperiodically. Unlike their earlier tiles—the "hat" and the "turtle"—this tile, which the authors call a "spectre" does not require any tiles to be flipped upside down in order to tile the plane aperiodically. (In fact, if we allow reflections, then it is possible to tile the plane periodically with the spectre tile.)
I have been down a rabbit hole of metallic ratios today. You have heard of the golden ratio, but how about the silver ratio? The bronze ratio? There is a whole family of ratios. real solutions to:
Golden: x^2=x+1
Silver: x^2=2x+1
Bronze: x^2=3x+1
the whole family: x^2=nx+1
Plastic: x^3=x+1 (see Harriss spiral)
SuperGolden: x^3=x^2+1
Do you know of any others?
Peter Rowlett
Mike McHargue
John Golden
Ben Werdmuller
Dave Richeson
Christian Lawson-Perfect