Solving Geometric Puzzles: Prisms & Balloons, Polygons & Tension

[sebassen]

Hi everyone, I've been thinking about these questions and would like to know if you can come up with their answers:

1. if you attach prisms to a balloon and inflate it, will the prisms make it impossible to keep inflating it at some time? Talking about "formulas", why?

2. why do grounds made with prisms ("polygonal granoblastic texture") have less superficial tension than any other ground?

Thx a lot,

Sebassen

 

[Simon Bridge]

1. depends on the prisms and how they are attached.
2. because they have more meaningful tensions and, being quite serious structures, cannot be bothered with anything superficial. The resulting coffee is no help.
... this is why you need to provide a context for your questions.

 

[sebassen]

1. the prisms have hexagonal base and are glued to the balloon. Then, as you inflate the balloon, they assemble.
2. xD
I'm trying to understand basalt columns, whether they are hexagonal for allowing expansion or whaat

 

[Simon Bridge]

Well hexagons tessellate to a flat surface.
Can you provide an example?

Of course if you inflate a balloon inside a structure designed to become rigid at some point in the inflation then of course that would restrict the amount the balloon can inflate. Like I could cover it in interlocking steel plates.

"Superficial tension" would be surface tension to everyone else right?
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html

Basalt column like at Giant's Causway are not predominantly hexagonal - go look at some. The mean number of sides is, indeed, six - but when you look at them and walk over them the "hexagonalness" is not particularly striking.
[see: D. Weaire and N. Rivier. Contemporary Physics 25 1 (1984), pp. 55-99]

More accessible discussion:
http://giantcrystals.strahlen.org/europe/basalt.htm

 

[PJC01]

Hello Sebassen,

Thank you for sharing your thoughts on geometric puzzles involving prisms and balloons, as well as polygons and tension. I find these questions quite intriguing and would be happy to provide some insights on them.

1. If you attach prisms to a balloon and inflate it, will the prisms make it impossible to keep inflating it at some time?

The answer to this question depends on several factors, such as the size and weight of the prisms, the material of the balloon, and the amount of air being pumped into the balloon. In general, adding prisms to a balloon will increase its weight and reduce its overall elasticity, making it more difficult to inflate. However, whether it becomes impossible to inflate at some point will also depend on the strength of the material and the amount of air pressure the balloon can withstand before bursting. As for "formulas", there are various equations that can be used to calculate the force and pressure exerted on the balloon as it is being inflated, taking into account the weight and shape of the prisms.

2. Why do grounds made with prisms ("polygonal granoblastic texture") have less superficial tension than any other ground?

This is an interesting question and I would like to clarify that "polygonal granoblastic texture" is not a commonly used term in the scientific community. However, based on my understanding, it could refer to a type of ground made up of polygonal shaped prisms, similar to a crystal structure. In this case, the reason for the reduced surface tension could be due to the overall shape and arrangement of the prisms, which allows for more space between them and therefore less contact and tension between the surfaces. Additionally, the material of the prisms could also play a role in reducing surface tension. Further research and experimentation would be needed to fully understand the phenomenon.

I hope this helps to answer your questions. Keep exploring and thinking about these types of puzzles, as they can lead to interesting scientific discoveries. Best of luck!

Sincerely,