双曲面隧道，单叶双曲面结构

Hyperboloidal Tunnel, One-Sheeted Hyperboloid

2024-03-16 01:48:39

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Summary

Hyperboloidal Tunnel, One-Sheeted Hyperboloid

The hyperboloid (of one sheet) is an interesting ruled surface. Using two sticks (such as pencils), one can model it in the classroom. It is aesthetically appealing and mathematically rich. I got this design idea after a recent iteration of my spin-the-cube lesson. It is pedagogically dissected to show different aspects of the structure. It comes with two pieces. The top part is a hyperboloidal chamber with a 120-degree and a 90-degree cut, revealing both the surfaces and curves. The bottom part functions like a turntable demonstrating the ruled nature of the hyperboloid. The ruling is either a segment of a pencil, up to 100 mm, or the integrated bar.

References

Bu, Lingguo (2021) "The Spinning Cube: An Algebraic Excursion," The Mathematics Enthusiast: Vol. 18 : No. 1 , Article 5. DOI: https://doi.org/10.54870/1551-3440.1512
https://en.wikipedia.org/wiki/Hyperboloid

Print Settings

Printer brand:
FlashForge
Printer:
Finder
Rafts:
No
Supports:
No
Resolution:
.2
Infill:
25%
Filament brand:
n/a
Filament color:
n/a
Filament material:
PLA or PETG
Notes:
Turn off cooling fan for the first few layers if possible to improve bed adhesion.