Mathematical Balloon Twisting

“Balloon twisting is fun” – and may also have industrial and military applications in the construction of so-called Air Beams – but some might say that the mathematics behind balloon twisting has, until recently, been under represented in the academic literature.

To counter this, the authors of the paper ‘Computational Balloon Twisting: The Theory of Balloon Polyhedra’ introduce the idea of ‘Bloons’ – which are mathematical idealisations of real-world balloons (see doggie balloon and its associated bloons above). The research not only provides “…algorithms to find the fewest balloons that can make exactly a desired graph or, using fewer balloons but allowing repeated traversal or shortcuts, the minimum total length needed by a given number of balloons.” But also, in contrast, shows that “…NP-completeness of determining whether such an optimal construction is possible with balloons of equal length.” Although the paper makes great strides towards a full theory of balloon twisting there are still at least two outstanding enigmas.
[1] It remains open to find interesting polyhedra that fail to have a twisting from a bloon number of equal-length bloons but not by virtue of indivisibility.
[2] It also remains open whether some symmetric polyhedron can be twisted only from nonidentical units or only from units arranged asymmetrically.

The paper,‘Computational Balloon Twisting:The Theory of Balloon Polyhedra’ was published as part of the Proceedings of the 20th Canadian Conference on Computational Geometry (CCCG 2008), Montréal, Québec, Canada, August 2008.

Also see : Co-author Vi Hart’s extensive webpages on Mathematical Balloon Twisting

BONUS: Co-author Erik Demaine is a member of the Luxuriant Flowing Hair Club for Scientists (LFHCfS).

75 Responses to “Mathematical Balloon Twisting”

  1. {NEW✅ ROBLOX HACKEXPLOIT✅ LAXIFY 😱 OP JAILBREAK CMDS Says:

    I dugg some of you post as I thought they were very beneficial invaluable

  2. Too many cooks Says:

    These two better settle their score now before everything ends up burnt!

  3. Too many cooks Says:

    These two better settle their score now before everything ends up burnt!

  4. Homestays in varanasi Says:

    This is one awesome post.Really thank you! Fantastic.

  5. Google Says:

    One of our guests just lately proposed the following website.

  6. xerox printer drivers Says:

    Great blog.Thanks Again. Great.

  7. Can you hear me now Says:

    This guy has something very important to say!

  8. Can you hear me now Says:

    This guy has something very important to say!

  9. Couple has the best seat in the house Says:

    These two sure know how to enjoy a movie!

  10. Couple in movie theater Says:

    This has to be the happiest couple on planet Earth!

  11. Couple in movie theater Says:

    This has to be the happiest couple on planet Earth!

  12. Couple has the best seat in the house Says:

    These two sure know how to enjoy a movie!

  13. Old guy reads the newspaper on a beautiful sunny day Says:

    Nothing relaxes him like reading does.

  14. Relaxing while reading the newspaper Says:

    Nothing makes him more happy than reading a newspaper underneath a tree.

  15. Even doctors like chocolate Says:

    Nothing is more relaxing than eating chocalate!

  16. The future of kitty cats Says:

    This is what the future holds for kitty cats.

  17. He likes to be their first customer in the morning Says:

    Expect to see him when the restaurant opens every day.

  18. Even doctors like chocolate Says:

    Nothing is more relaxing than eating chocalate!

  19. tri-cities real estate Says:

    Looking forward to reading more. Great post.Thanks Again. Really Cool.

  20. Kitty Futurology Says:

    This is the future of kitty cats.

  21. The future of kitty cats Says:

    This is what the future holds for kitty cats.

  22. He likes to be their first customer in the morning Says:

    Expect to see him when the restaurant opens every day.

  23. Kitty Futurology Says:

    This is the future of kitty cats.

  24. Doctor enjoying chocolate Says:

    Doctor bite right into a chococlate bar.

  25. Doctor enjoying chocolate Says:

    Doctor bite right into a chococlate bar.

Leave a Reply