Sierpinski Tetrahedron
Source
G4G14
Title
Sierpinski Tetrahedron
Creator
Contributor
Hideki Tsuiki
Subject
Art
Recreational Math
Description
A 3D-printed copy of the 5th-level (i.e., 1024 tetrahedrons) approximation of the Sierpinski Tetrahedron.
Please enjoy the beautiful shadows under sunshine.
In particular, this object has projections with positive measure and the shadow contains an openset from some directions.
Such direction is characterized as follows.
Let A, B, C, D be the images of the four vertices and let x and y be AB = x AC + y AD.
The shadow has a positive Lebesgue measure if and only if x and y are rationals of the form p/q for odd numbers p and q.
Please enjoy the beautiful shadows under sunshine.
In particular, this object has projections with positive measure and the shadow contains an openset from some directions.
Such direction is characterized as follows.
Let A, B, C, D be the images of the four vertices and let x and y be AB = x AC + y AD.
The shadow has a positive Lebesgue measure if and only if x and y are rationals of the form p/q for odd numbers p and q.
Identifier
G14-012
Collection
Citation
“Sierpinski Tetrahedron,” G4G Gift Exchange Archive, accessed April 20, 2024, https://g4gexchangearchive.omeka.net/items/show/645.
Comments