Sierpinski Tetrahedron

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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.

Identifier

G14-012

Collection

Citation

“Sierpinski Tetrahedron,” G4G Gift Exchange Archive, accessed May 21, 2024, https://g4gexchangearchive.omeka.net/items/show/645.

Comments

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