This document discusses geodesics in differential geometry. It begins with an introduction to geodesics, defining them as curves that locally minimize distance between points on a mathematically defined space, like a straight line on a curved surface. It then provides examples of geodesics on spheres and cylinders. Geodesics on spheres are great circles, while geodesics on cylinders are intersections with planes. The document suggests geodesics could help plan surgical paths and describes studying geodesics to find shortest paths on surfaces. It concludes by emphasizing the importance of understanding differential geometry concepts like geodesics.

1. Boonnam Nathaphon
ブンナム ナッタポン
Physical and Mathematical Studies
School of Science andTechnology
nut4297nb@gmail.com

2. Motivation
What is GEODESIC ?
Applications
Conclusion
Differential Geometry: GEODESICS Midterm Presentation

3. Reference site : http://www.hflight.net /
Differential Geometry: GEODESICS Midterm Presentation

4. GEODESICS
 a generalization of the notion of a straight
line to curved spaces.
 a curve locally minimizes the distance
between two points on any mathematically
defined space.
Differential Geometry: GEODESICS Midterm Presentation

5. Differential Geometry: GEODESICS Midterm Presentation

6.  The world-shaped geometry is similar to the sphere.
 The shortest path is the intersection of plane and
sphere; great circle.
Differential Geometry: GEODESICS Midterm Presentation

7. Reference site : http://62mileclub.com/ Reference site : http://health.howstuffworks.com
Reference site : http://www.umm.edu/
Differential Geometry: GEODESICS Midterm Presentation

8. If we look at arm-shaped
geometry similar to the
cylinder, we will be able
to find the shortest path
in the surgery .
Differential Geometry: GEODESICS Midterm Presentation

9. If we take the both of a
cylinder and a cone to
stick together and find
geodesic path, it would
be applied.
Differential Geometry: GEODESICS Midterm Presentation

10. Differential Geometry: GEODESICS Midterm Presentation

11. Differential Geometry: GEODESICS Midterm Presentation

12. Differential Geometry: GEODESICS Midterm Presentation

13.  Before we have done the other applications as
above, we have to know about the notion of
differential geometry
 In particular, if we want to find the shortest
path between two points on any surfaces.
 WE SHOULD STUDYTHE GEODESICS.
Differential Geometry: GEODESICS Midterm Presentation

14. FOR YOUR ATTENTION

15. Boonnam Nathaphon
ブンナム ナッタポン
Physical and Mathematical Studies
School of Science andTechnology
nut4297nb@gmail.com