Prompt:
An icosahedron face-inscribes in an octahedron. when do we first find depictions of this in civilization?
Google in AI mode:
The first known depictions and mathematical descriptions of an icosahedron inscribed inside an octahedron appear during the Italian Renaissance in the late 15th century, specifically in the works of the painter and mathematician Piero della Francesca. [1]
While the ancient Greeks discovered the Platonic solids individually—and Euclid's Elements investigated nesting relationships like a cube inside a dodecahedron—the specific relationship of a regular icosahedron sharing faces with an enclosing octahedron was not detailed until the Renaissance revival of geometry. [1, 2, 3]
Wow, Piero della Francesca! He's already a superstar in our School of Tomorrow curriculum as he came up with that nifty formula for deriving the volume of a tetrahedron from its six edges.
Put in any six edges in the right order, that make a legal tetrahedron (any of the BEAST mods for example) and out comes the corresponding volume.
What we did in the Python version is add in S3 and simplify the computations accordingly.
I'd link to the relevant Notebook(s) now but GitHub seems to have borked its notebook display function, we hope temporarily, thereby making my million dollar curriculum (free to clone) inaccessible to the casual viewer.
Let's hope they fix the bug, as a great many peeps use Jupyter Notebooks to share curriculum.
I recommend such Notebooks to anyone into showing computations alongside text and figures, along with version control more generally.
I know what I can do instead: pull it up in colab.research.google and save it in my Google Drive:
https://colab.research.google.com/drive/16Q85p4YU4f5AsA2L65ypMQJSHqyBprEl?usp=sharingThere's lots more info in the saved query BTW:
https://share.google/aimode/VA68IqZjF3cMIDwx5
