How can billiard be used to illustrate any laws of mathematics?

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SUMMARY

Billiards serves as a practical illustration of various mathematical laws, particularly the principle that the angle of incidence equals the angle of reflection. In an elliptical billiard table, the motion of the balls is deterministic, while the dynamics become chaotic with more than three balls on a standard table. Circular billiard tables also exhibit chaotic behavior. These concepts have implications in fields such as quantum cryptography, as noted in the works of Yuri Suhov. Additionally, the game highlights the human capacity for skill acquisition through repetition, contrasting human performance with that of machines.

PREREQUISITES
  • Understanding of geometric principles, specifically angles and reflections.
  • Familiarity with deterministic and chaotic systems in mathematics.
  • Basic knowledge of quantum cryptography concepts.
  • Insights into skill acquisition and motor learning theories.
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  • Research the mathematical principles of reflection and incidence in physics.
  • Explore deterministic versus chaotic systems in mathematical modeling.
  • Study the implications of billiards in quantum cryptography, focusing on Yuri Suhov's papers.
  • Investigate theories of motor learning and skill acquisition in sports.
USEFUL FOR

This discussion is beneficial for mathematicians, physicists, educators, and anyone interested in the intersection of mathematics and physical games like billiards.

Thallium
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I indulged in a billiard match on Euro Sport and it got me wondering. How can billiard be used to illustrate any laws of mathematics?
 
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well it would only be approximate because of the inherent imperfection of models over theory, but you could demonstrate that the angle of incidence equals the angle of reflection, if the billiard table were elliptic then the motion is deterministic, if there are more than three balls on an ordinary table it is chaotic, circular tables are also i think chaotic (these ideas arise in (quantum) cryptography etc but i can only point you at the relevant papers (yuri suhov i think)), and general mechanics laws up to a point.
it also demonstrates the amazing ability of the human mind and body to learn through repetition - despite the seemingly easy nature of the game, in simple terms of potting of snooker (not european billiards perhaps), machines are incredibly bad at it.
 

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