curvature and torsion for final presentation

50
ن م ح ر ل ه ا ل ل م ا س ب م ي ح ر ل ا

Upload: ibrahim-hamad

Post on 13-Feb-2017

175 views

Category:

Documents


4 download

TRANSCRIPT

Page 1: Curvature and Torsion for final presentation

بسم الله الرحمن الرحيم

Page 2: Curvature and Torsion for final presentation

GeneralizedGeneralized

Curvature and Torsion Curvature and Torsion inin

Nonstandard AnalysisNonstandard Analysis

Page 3: Curvature and Torsion for final presentation
Page 4: Curvature and Torsion for final presentation
Page 5: Curvature and Torsion for final presentation
Page 6: Curvature and Torsion for final presentation
Page 7: Curvature and Torsion for final presentation
Page 8: Curvature and Torsion for final presentation
Page 9: Curvature and Torsion for final presentation
Page 10: Curvature and Torsion for final presentation
Page 11: Curvature and Torsion for final presentation
Page 12: Curvature and Torsion for final presentation
Page 13: Curvature and Torsion for final presentation
Page 14: Curvature and Torsion for final presentation
Page 15: Curvature and Torsion for final presentation
Page 16: Curvature and Torsion for final presentation
Page 17: Curvature and Torsion for final presentation
Page 18: Curvature and Torsion for final presentation
Page 19: Curvature and Torsion for final presentation
Page 20: Curvature and Torsion for final presentation
Page 21: Curvature and Torsion for final presentation

C

B

T

A

Page 22: Curvature and Torsion for final presentation
Page 23: Curvature and Torsion for final presentation
Page 24: Curvature and Torsion for final presentation
Page 25: Curvature and Torsion for final presentation
Page 26: Curvature and Torsion for final presentation
Page 27: Curvature and Torsion for final presentation
Page 28: Curvature and Torsion for final presentation
Page 29: Curvature and Torsion for final presentation
Page 30: Curvature and Torsion for final presentation
Page 31: Curvature and Torsion for final presentation
Page 32: Curvature and Torsion for final presentation
Page 33: Curvature and Torsion for final presentation
Page 34: Curvature and Torsion for final presentation
Page 35: Curvature and Torsion for final presentation
Page 36: Curvature and Torsion for final presentation
Page 37: Curvature and Torsion for final presentation
Page 38: Curvature and Torsion for final presentation
Page 39: Curvature and Torsion for final presentation
Page 40: Curvature and Torsion for final presentation
Page 41: Curvature and Torsion for final presentation
Page 42: Curvature and Torsion for final presentation
Page 43: Curvature and Torsion for final presentation
Page 44: Curvature and Torsion for final presentation
Page 45: Curvature and Torsion for final presentation
Page 46: Curvature and Torsion for final presentation

86420-2-4-6-8-10

6

4

2

0

-2

-4

-6

86420-2-4-6-8-10

6

4

2

0

-2

-4

-6

86420-2-4-6-8-10

6

4

2

0

-2

-4

-6

86420-2-4-6-8-10

6

4

2

0

-2

-4

-6

a=-6.3 (family of 99 , step 0.12 )

y= a2-12a x+ a2+1

2a

x̂ 2+y 2̂=1

Page 47: Curvature and Torsion for final presentation

6420-2-4-6-8-10-12

6

4

2

0

-2

-4

6420-2-4-6-8-10-12

6

4

2

0

-2

-4

6420-2-4-6-8-10-12

6

4

2

0

-2

-4

6420-2-4-6-8-10-12

6

4

2

0

-2

-4a=-6 (family of 99 , step 0.12 )

y= 1a x- 1/4a2+1

a

x+y 2̂=1

Page 48: Curvature and Torsion for final presentation
Page 49: Curvature and Torsion for final presentation
Page 50: Curvature and Torsion for final presentation

generalized generalized

Curvature and TorsionCurvature and Torsion inin

Nonstandard AnalysisNonstandard Analysis