1 / 44

Topology: Finding the Shape of the Universe

Topology: Finding the Shape of the Universe. A presentation by: Fionnghuala Eley O’Reilly Megan Gage Jene é Dampier Kenmond Pang. The Goal. The Goal. Finding the shape of the universe. The Goal. Finding the shape of the universe Takes a substantial amount of math. The Goal.

mauve
Download Presentation

Topology: Finding the Shape of the Universe

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Topology: Finding the Shape of the Universe A presentation by: Fionnghuala Eley O’Reilly Megan Gage Jeneé Dampier Kenmond Pang

  2. The Goal

  3. The Goal • Finding the shape of the universe

  4. The Goal • Finding the shape of the universe • Takes a substantial amount of math

  5. The Goal • Finding the shape of the universe • Takes a substantial amount of math • Uses a large amount of math

  6. The Goal • Finding the shape of the universe • Takes a substantial amount of math • Uses a large amount of math • Encountered problems

  7. Problems We Faced

  8. Problems We Faced • Is it even possible to figure out the shape of the universe if we live in it?

  9. Problems We Faced • Is it even possible to figure out the shape of the universe if we live in it? • How could we tell its shape from the inside?

  10. Topology

  11. Topology • Shape and preserving the figure

  12. Topology • Shape and preserving the figure • Geometry vs. Topology

  13. Topology • Shape and preserving the figure • Geometry vs. Topology • Why is it important in our problem?

  14. Classification

  15. Classification • Dimensional Classification

  16. Classification • Dimensional Classification • The Zeroth Dimension

  17. Classification • Dimensional Classification • The Zeroth Dimension • A point

  18. Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension

  19. Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • Lines and circles

  20. Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • The Second Dimension

  21. Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • The Second Dimension • Squares and polygons

  22. Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • The Second Dimension • The Third Dimension

  23. Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • The Second Dimension • The Third Dimension • Cubes and polyhedra

  24. Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • The Second Dimension • The Third Dimension • The Fourth Dimension

  25. Classification • Dimensional Classification • Classifying Figures

  26. Classification • Dimensional Classification • Classifying Figures • “Dividing by 2”

  27. Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • Points divide lines

  28. Classification

  29. Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • Points divide lines • Lines divide polygons

  30. Classification

  31. Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • Points divide lines • Lines divide polygons • Polygons divide polyhedra

  32. Classification A cube is 3 dimensional because it can be split in two by a polygon.

  33. Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • Points divide lines • Lines divide polygons • Polygons divide polyhedra • Ultimately helps classify shapes

  34. Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • The Euler Characteristic

  35. Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • The Euler Characteristic • The Greek letter χ (chi)

  36. Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • The Euler Characteristic • The Greek letter χ (chi) • χ=f+p-e

  37. Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • The Euler Characteristic • The Greek letter χ (chi) • χ=f+p-e • Our conclusions:

  38. Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • The Euler Characteristic • The Greek letter χ (chi) • χ=f+p-e • Our conclusions: • Polyhedra, polygons, annuli, etc.

  39. Classification • Why is classification important? • Narrows which shapes are possibilities

  40. Classification • Why is classification important? • Narrows which shapes are possible

  41. Conclusion • Goal

  42. Conclusion • Goal • Classification

  43. Conclusion • Goal • Classification • The Euler Charactersitic

  44. Conclusion • Goal • Classification • The Euler Characteristic • What comes next?

More Related