The Sum of Squares in Polycubes (Media Exposition)

Author Donald R. Sheehy



PDF
Thumbnail PDF

File

LIPIcs.SoCG.2023.65.pdf
  • Filesize: 3.43 MB
  • 6 pages

Document Identifiers

Author Details

Donald R. Sheehy
  • North Carolina State University, Raleigh, NC, USA

Cite As Get BibTex

Donald R. Sheehy. The Sum of Squares in Polycubes (Media Exposition). In 39th International Symposium on Computational Geometry (SoCG 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 258, pp. 65:1-65:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.SoCG.2023.65

Abstract

We give several ways to derive and express classic summation problems in terms of polycubes. We visualize them with 3D printed models. The video is here: http://go.ncsu.edu/sum_of_squares.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Archimedes
  • polycubes
  • sum of squares

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. Archimedes. On Spirals, pages 151-188. Cambridge Library Collection - Mathematics. Cambridge University Press, 2009. URL: https://doi.org/10.1017/CBO9780511695124.014.
  2. Gill Barequet and Mira Shalah. Automatic Proofs for Formulae Enumerating Proper Polycubes. In Lars Arge and János Pach, editors, 31st International Symposium on Computational Geometry (SoCG 2015), volume 34 of Leibniz International Proceedings in Informatics (LIPIcs), pages 19-22, Dagstuhl, Germany, 2015. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik. URL: https://doi.org/10.4230/LIPIcs.SOCG.2015.19.
  3. Martin Gardner. More about the shapes that can be made with complex dominoes (mathematical games). Scientific American, 203(5):186-201, November 1960. Google Scholar
  4. Solomon W. Golomb. Polyominoes: Puzzles, Patterns, Problems, and Packings - Revised and Expanded Second Edition. Princeton University Press, Princeton, 1994. URL: https://doi.org/doi:10.1515/9780691215051.
  5. Ronald L. Graham, Donald E. Knuth, and Oren Patashnik. Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley, Reading, 1989. Google Scholar
  6. W. F. Lunnon. Counting multidimensional polyominoes. The Computer Journal, 18(4):366-367, January 1975. URL: https://doi.org/10.1093/comjnl/18.4.366.
  7. Donald R. Sheehy. polycube. https://github.com/donsheehy/polycube, 2023. Google Scholar
  8. Man-Keung Siu. Proof without words: Sum of squares. Mathematics Magazine, 57(2):92-92, 1984. URL: https://doi.org/10.1080/0025570X.1984.11977083.
  9. The CGAL Project. CGAL User and Reference Manual. CGAL Editorial Board, 5.5.2 edition, 2023. URL: https://doc.cgal.org/5.5.2/Manual/packages.html.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail