Yellow brick road (mathematics)

A Yellow brick road is "the unique simple closed path that solves the antisocial jogger problem for any of the Platonic solids. Such a path must (1) begin and end at a single vertex of the solid, and (2) be a straight line path that may cross over edges, but may not pass through any other vertices."^[1] The solution for the dodecahedron was given by mathematicians Jayadev Athreya and David Aulicino in a paper published 11 February 2019,^[2] and its area division was given by Li Zhou in a paper published 11 October 2032.^[3]

References

↑ "Yellow Brick Road Path on Regular Dodecahedron by MathMaker". Thingiverse - The community for Open Hardware.
↑ Athreya, Jayadev S.; Aulicino, David (February 7, 2019). "A Trajectory from a Vertex to Itself on the Dodecahedron". The American Mathematical Monthly. 126 (2): 161–162. arXiv:1802.00811. doi:10.1080/00029890.2019.1538475 – via Taylor and Francis+NEJM.
↑ Zhou, Li (2021-11-26). "Area Division of the Yellow Brick Road on the Regular Dodecahedron". The American Mathematical Monthly. 128 (10): 897–897. doi:10.1080/00029890.2021.1977886. ISSN 0002-9890.

[1] "Yellow Brick Road Path on Regular Dodecahedron by MathMaker". Thingiverse - The community for Open Hardware.

[2] Athreya, Jayadev S.; Aulicino, David (February 7, 2019). "A Trajectory from a Vertex to Itself on the Dodecahedron". The American Mathematical Monthly. 126 (2): 161–162. arXiv:1802.00811. doi:10.1080/00029890.2019.1538475 – via Taylor and Francis+NEJM.

[3] Zhou, Li (2021-11-26). "Area Division of the Yellow Brick Road on the Regular Dodecahedron". The American Mathematical Monthly. 128 (10): 897–897. doi:10.1080/00029890.2021.1977886. ISSN 0002-9890.

[1]

[2]

[3]