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Ghanakruti mattu jalagalu

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Karnataka OER

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???? ? ????? ? ????????????? . ? ?????? ????????? ? ???? ?????? ????????? ? ?????????? ????? ???? ? ?????? ? ??????? ?????? ? ??????? ????? ???? ? ???? ??????? ? ????????? ??? ???????? .
????? ? ???? ?? ??? ?????? ??????????? ???????????????? ??????? ????????????? . ??????? ????????? ???? ??????? ???? ?????? ??? ??????? ??????? ???????
????????????? ? ??? ????????? ?????????? ????? ?????????? ????. ? ???:- ????????? ???????????? ????????
?????? ?????? ???? ??????? & ?????????? ??????? ?????????? ???????????? ???????. ???:-
???? ?????? ????????? ???? ?????? ??????? ???? ?????? ??? ?? ???? ?????????????? ????? ???? ?????? ????????? ???????. ???:- ??????? ?? ????? ?? ?????? ?? ??????? ?? ???? ??
1. ??????? ?? (4 ????? ??) ?????? ???? ??? ??????? ???? (?????? ????? ) 1 2 3 4
2. ????? ?? (6 ????? ??) ? ?????? ???? ??? ??????? ???? ( ???) 1 2 3 4 5 6
3. ?????? ?? (8 ????? ??) ? ?????? ???? ??? ??? ???? ???? (?????? ????? ) 1 2 3 4 5 6 7 8
4.????? ??? ?? (12 ????? ??) ? ?????? ???? ??? ??? ???? ???? (???? ??????) 1 2 3 4 5 6 7 8 9 10 11 1 2
5.???? ?? (20 ????? ??) ? ?????? ???? ??? ??? ???? ???? (?????? ????? )
?????? ??????? ??? ? ???? ??? ? ?????? ????? ???? ???????????? ?? ??????? ????????? ??????????? ??? ?????? ???? ?? ??????? ????????? ????????? ?? ?????? ???????? ????? ???????
??? ? ??????????? ??? ? ??? ??????? ?????? . ??????????? ??????????? ?????????????? ??? ????? ???? ????? ??. ??? ???? ?????????????? ????? ???????????? ????????????? ??? ? ?????.
= ????? ????? = ?????? ????? = ?????? ????? ???????? ?????? ??? ?? ??? ? F + V = E + 2 F V E
32=32301220????? ?? 32=32302012????????? ?? 14=141268?????? ???? ?? 14=141286????????? ?? 4+4=6+2 8=8 644???????????? ?? F+V=E+ 2 Number of Edges ( E ) Vertces ( V) Number of Faces ( F) ??????? ??? ? ??????????????? ???????
? ????? ???????? ????? ???? ?????????.
Ghanakruti mattu jalagalu
.???????? ????? .???? ??? ????? ????? .???? ???? .???? ??? ????????? ?? ????? ? ???????????????? ?????????? ??????????? ???????????????????? ??????? ????????????.(GRAPHS ) ???????
????? ?????????? ? ???? ???????? ???? ?????????????? ????????????? ??? ????????, ????????? ??? ????? ???? ???? ??????????? . (NODES ) ? ??????? ????? ????????? ????????????? ??????? ????????????? ??? ????????? ??????????? . (ARCS ) ? ??????? ?????????? ?????????? (?????? ?????????? ????) ??? ???? ??????????? . .(REGION)
A C B ?????? ??????????? = ???????? = ??????? = 3 4 3
? ????? ???? ????? ?????? , ????? ????? ????????? ????? R P SQ
??????? ????? ???? ? N+R = A+2 ? N=????? ??????? . ? R=?????? . ? A=?????? .
? ????? ?????? ????? ???? ???? ?????????? R P SQ N=4 R=5 A=7 N+R = A+2 4+5 = 7+2 9 = 9 ??? ?? ??? ? ?????? ??????????? ???????. ????????.
??????? ?????? ?????? ??????? ??????? ????????????? ????????? ???????????????? ????? ?????? ???? ???????????? ??? ?????? ?? ?????????? ??? ??? ??????? ??? ?????? ????????????. ??:-
????? ?????? ??? ? ???? ????? ???????? ????????????? ???? ? ???????? ??????????? ????? ????????? ? ??????????? ??? ???? ???????????. ???:- C BA D ??? ?????? A ? ?? = 3 ??? ??????B ? ?? = ??? ??????C ? ?? = 2 3 ??? ??????D ? ?? = 2
????? ????? ?????? ???. ? ???? ???????? ???? ??????? ??????? ??????? ????? ???? ?????????? . ?????? A ????? ?????? ??? 2 A
?? ????? ??????? & ??? ????? ??????? ??? ?????? A ? ?? = 4 A CD B ??? ?????? B ? ?? = 3 ??? ?????? C ? ?? = 4 ??? ?????? D ? ?? = 3 (?? ?????? ??????? ) (??? ?????? ??????? ) (?? ?????? ??????? ) (??? ?????? ??????? ) ???? ??????? ??? ???? ???? ??????? ????? ??? ?????? ???????????????? ?????????.
??????????? ????? ????? ? ????? ??????? ??????? ???? ??????? . ? ????? ????? ????? ???? ??? ????? ??????? ???????. ? ???? ?????? ??????? ????? ??? ????? ??????????, ??? ??????? ????????? .
?????? ???? ??????? ????? ??????? ????? . ?????????? ???????? ???? ????? ???? ???? ??????? ??????? ???? ??? ????????????? .???? ??? ???????????? ????? ??????? ??? ??????????? ??????? ????? ?? ??????????? ????? ????????? .???? ??? ??????????. ? ????????? ?????? ????????? . ???????? ???????? ??? ???????????? ???????? ?????????? ????????
??????? ??????? ?????? ?????? ? D A B C QP S R D C BE A
???? ???????? A B C 2 22 2 0 2 2 2 0 A A B B C C 2 2 2 2 0 2 2 2 0
????????? ???? ???? 0 2 2 2 0 1 2 1 0 A A B B C C A B C 0 2 2 2 0 1 2 1 0
???????? 1. ??????? ??? ??? ???? ???? 2. ?????? ?? ???? ? ????????? ????????????? ??????? ????????????? ______________???????. 3. ?????? A ????? ?????? ??? __________ 4. ??????? ????? ???? __________________. 5. ??????? ??? ???? ????? ????? A A) ??? B) ??? C) ??????????? A) N+R=A+2 B) N+A=R+2 C) A+R=N+2 A) 8 B) 6 C) 4 A) ?????? B) ??? C) ??????? ????????? A) 1 B) 2 C) 3
?????? 10 ??? ???? ??? ?????. www.google.com www.math.com www.3quarks.com www.wikipedia.com
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Ghanakruti mattu jalagalu
Ghanakruti mattu jalagalu

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Ghanakruti mattu jalagalu

  • 3. ???? ? ????? ? ????????????? . ? ?????? ????????? ? ???? ?????? ????????? ? ?????????? ????? ???? ? ?????? ? ??????? ?????? ? ??????? ????? ???? ? ???? ??????? ? ????????? ??? ???????? .
  • 4. ????? ? ???? ?? ??? ?????? ??????????? ???????????????? ??????? ????????????? . ??????? ????????? ???? ??????? ???? ?????? ??? ??????? ??????? ???????
  • 5. ????????????? ? ??? ????????? ?????????? ????? ?????????? ????. ? ???:- ????????? ???????????? ????????
  • 6. ?????? ?????? ???? ??????? & ?????????? ??????? ?????????? ???????????? ???????. ???:-
  • 7. ???? ?????? ????????? ???? ?????? ??????? ???? ?????? ??? ?? ???? ?????????????? ????? ???? ?????? ????????? ???????. ???:- ??????? ?? ????? ?? ?????? ?? ??????? ?? ???? ??
  • 8. 1. ??????? ?? (4 ????? ??) ?????? ???? ??? ??????? ???? (?????? ????? ) 1 2 3 4
  • 9. 2. ????? ?? (6 ????? ??) ? ?????? ???? ??? ??????? ???? ( ???) 1 2 3 4 5 6
  • 10. 3. ?????? ?? (8 ????? ??) ? ?????? ???? ??? ??? ???? ???? (?????? ????? ) 1 2 3 4 5 6 7 8
  • 11. 4.????? ??? ?? (12 ????? ??) ? ?????? ???? ??? ??? ???? ???? (???? ??????) 1 2 3 4 5 6 7 8 9 10 11 1 2
  • 12. 5.???? ?? (20 ????? ??) ? ?????? ???? ??? ??? ???? ???? (?????? ????? )
  • 13. ?????? ??????? ??? ? ???? ??? ? ?????? ????? ???? ???????????? ?? ??????? ????????? ??????????? ??? ?????? ???? ?? ??????? ????????? ????????? ?? ?????? ???????? ????? ???????
  • 14. ??? ? ??????????? ??? ? ??? ??????? ?????? . ??????????? ??????????? ?????????????? ??? ????? ???? ????? ??. ??? ???? ?????????????? ????? ???????????? ????????????? ??? ? ?????.
  • 15. = ????? ????? = ?????? ????? = ?????? ????? ???????? ?????? ??? ?? ??? ? F + V = E + 2 F V E
  • 16. 32=32301220????? ?? 32=32302012????????? ?? 14=141268?????? ???? ?? 14=141286????????? ?? 4+4=6+2 8=8 644???????????? ?? F+V=E+ 2 Number of Edges ( E ) Vertces ( V) Number of Faces ( F) ??????? ??? ? ??????????????? ???????
  • 17. ? ????? ???????? ????? ???? ?????????.
  • 19. .???????? ????? .???? ??? ????? ????? .???? ???? .???? ??? ????????? ?? ????? ? ???????????????? ?????????? ??????????? ???????????????????? ??????? ????????????.(GRAPHS ) ???????
  • 20. ????? ?????????? ? ???? ???????? ???? ?????????????? ????????????? ??? ????????, ????????? ??? ????? ???? ???? ??????????? . (NODES ) ? ??????? ????? ????????? ????????????? ??????? ????????????? ??? ????????? ??????????? . (ARCS ) ? ??????? ?????????? ?????????? (?????? ?????????? ????) ??? ???? ??????????? . .(REGION)
  • 22. ? ????? ???? ????? ?????? , ????? ????? ????????? ????? R P SQ
  • 23. ??????? ????? ???? ? N+R = A+2 ? N=????? ??????? . ? R=?????? . ? A=?????? .
  • 24. ? ????? ?????? ????? ???? ???? ?????????? R P SQ N=4 R=5 A=7 N+R = A+2 4+5 = 7+2 9 = 9 ??? ?? ??? ? ?????? ??????????? ???????. ????????.
  • 25. ??????? ?????? ?????? ??????? ??????? ????????????? ????????? ???????????????? ????? ?????? ???? ???????????? ??? ?????? ?? ?????????? ??? ??? ??????? ??? ?????? ????????????. ??:-
  • 26. ????? ?????? ??? ? ???? ????? ???????? ????????????? ???? ? ???????? ??????????? ????? ????????? ? ??????????? ??? ???? ???????????. ???:- C BA D ??? ?????? A ? ?? = 3 ??? ??????B ? ?? = ??? ??????C ? ?? = 2 3 ??? ??????D ? ?? = 2
  • 27. ????? ????? ?????? ???. ? ???? ???????? ???? ??????? ??????? ??????? ????? ???? ?????????? . ?????? A ????? ?????? ??? 2 A
  • 28. ?? ????? ??????? & ??? ????? ??????? ??? ?????? A ? ?? = 4 A CD B ??? ?????? B ? ?? = 3 ??? ?????? C ? ?? = 4 ??? ?????? D ? ?? = 3 (?? ?????? ??????? ) (??? ?????? ??????? ) (?? ?????? ??????? ) (??? ?????? ??????? ) ???? ??????? ??? ???? ???? ??????? ????? ??? ?????? ???????????????? ?????????.
  • 29. ??????????? ????? ????? ? ????? ??????? ??????? ???? ??????? . ? ????? ????? ????? ???? ??? ????? ??????? ???????. ? ???? ?????? ??????? ????? ??? ????? ??????????, ??? ??????? ????????? .
  • 30. ?????? ???? ??????? ????? ??????? ????? . ?????????? ???????? ???? ????? ???? ???? ??????? ??????? ???? ??? ????????????? .???? ??? ???????????? ????? ??????? ??? ??????????? ??????? ????? ?? ??????????? ????? ????????? .???? ??? ??????????. ? ????????? ?????? ????????? . ???????? ???????? ??? ???????????? ???????? ?????????? ????????
  • 31. ??????? ??????? ?????? ?????? ? D A B C QP S R D C BE A
  • 32. ???? ???????? A B C 2 22 2 0 2 2 2 0 A A B B C C 2 2 2 2 0 2 2 2 0
  • 33. ????????? ???? ???? 0 2 2 2 0 1 2 1 0 A A B B C C A B C 0 2 2 2 0 1 2 1 0
  • 34. ???????? 1. ??????? ??? ??? ???? ???? 2. ?????? ?? ???? ? ????????? ????????????? ??????? ????????????? ______________???????. 3. ?????? A ????? ?????? ??? __________ 4. ??????? ????? ???? __________________. 5. ??????? ??? ???? ????? ????? A A) ??? B) ??? C) ??????????? A) N+R=A+2 B) N+A=R+2 C) A+R=N+2 A) 8 B) 6 C) 4 A) ?????? B) ??? C) ??????? ????????? A) 1 B) 2 C) 3
  • 35. ?????? 10 ??? ???? ??? ?????. www.google.com www.math.com www.3quarks.com www.wikipedia.com
  • 36. ?