Unraveling of a knotty mystery

PLAN
Diving into the problem
Mathematical model of knots
Experiment with color-changing fibers
Results and the application

DIVING INTO THE PROBLEM
https://www.dreamstime.com/illustration/dream-team.html?pg=7
https://www.vecteezy.com/free-vector/mountain-drawing?page=4
https://www.freepng.ru/png-huluqb/

MATHEMATICAL MODEL
A table of prime knots up to seven crossings
https://en.wikipedia.org/wiki/Knot_theory

COLOR-CHANGING FIBERS
http://news.mit.edu/2020/model-how-strong-knot-0102
https://www.scientificamerican.com/article/color-changing-fibers-unravel-a-knotty-mystery/
Trefoil knot, partially tightened

RESULTS
Conditions of knots’ stability:
a higher number of crossing points of two strands in contact
rotation of strand segments at neighboring crossing points in different directions
sliding of strands tangentially against each other
http://www.climbing.ru/media/all_2_2_1360/section_23_1_2_21/item_5433/
Zeppelin knot
Alpine butterfly knot

SUMMARY
Comprehension of the problem
Knot theory
Experiment with color-changing fibers
Results and the application