A Kornyushkin*

Moscow Institute of Physics and Technology, Russia

*Corresponding Author: A Kornyushkin, Moscow Institute of Physics and Technology, Russia.

Received: May 02, 2024; Published: June 06, 2025

Abstract

All closed normal movements of a ray of light in the mirror ellipse were classified by reducing them to regular polygons in the circle. This reduction leads to a collection of 12 related formulas based on just two integers: 2 and 14. To transition from a normal E-polygon (EP) to an arbitrary one, a new parameter t was used (which means, in essence, a normalized time).

Keywords: E-Polygon; Mirror Ellipse

References

1. A Kornyushkin. “Three New(?) Properties of an Ellipse and an Ellipsoid of Revolution (Computer Analysis)”. Current Trends in Computer Sciences and Applications (2022).
2. https://en.wikipedia.org/wiki/Pascal%27s_triangle
3. (9 ellipses).
4. (2 ellipses).
5. ₀T¹₀=(0,T,1,0) k=0.
6. ₁T’=(1,T’) k=1.
7. ⁽¹⁾₂E’=(1,2,E’) k=0.
8. ⁽¹⁾₃E’=(1,3,E’) k=1.
9. ⁽¹⁾₁E^c=(1,1,E,0,0) k=3.
10. (Type I-V).
11. ⁽¹⁾₃E’=(1,3,E’) k=1.
12. ⁽¹⁾₁E^c =(1,1,E,0,0) k=3.
13. ⁽¹⁾E^P=(1,E’) k=1.
14. ⁽¹⁾E*=(1,E*) k=2.
15. ⁽²⁾E*=(2,E*) k=2.
16. ⁽²⁾E^P=(2,E’) k=1.
17. ⁽¹⁾₂E’=(1,2,E’) k=0.
18. ⁽¹⁾ ₂e’=(1,2,e’) k=0.
19. ⁽²⁾ ₁e^c=(2,1,e,0,0) k=3.
20. ₂T^c=(2,T,0,0) k=1.
21. ₁T^c=(1,T,0,0) k=3.
22. ⁽¹⁾₁E³₄=(1,1,E,3,4) k=3.
23. (Program E-poly.exe).
24. Find regular sequences in circle.
25. Find regular sequences in ellipse (a=1.165).

Citation

Citation: A Kornyushkin. “Twelve Empirical Formulas for Reducing the Closed Motions of a Ray of Light in a Mirror Ellipse to the Case of a Circle".Acta Scientific Computer Sciences 7.4 (2025): 03-13.

Copyright

Copyright: © 2025 A Kornyushkin. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.