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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.
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Topology: Finding the Shape of the Universe A presentation by: Fionnghuala Eley O’Reilly Megan Gage Jeneé Dampier Kenmond Pang
The Goal • Finding the shape of the universe
The Goal • Finding the shape of the universe • Takes a substantial amount of math
The Goal • Finding the shape of the universe • Takes a substantial amount of math • Uses a large amount of math
The Goal • Finding the shape of the universe • Takes a substantial amount of math • Uses a large amount of math • Encountered problems
Problems We Faced • Is it even possible to figure out the shape of the universe if we live in it?
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?
Topology • Shape and preserving the figure
Topology • Shape and preserving the figure • Geometry vs. Topology
Topology • Shape and preserving the figure • Geometry vs. Topology • Why is it important in our problem?
Classification • Dimensional Classification
Classification • Dimensional Classification • The Zeroth Dimension
Classification • Dimensional Classification • The Zeroth Dimension • A point
Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension
Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • Lines and circles
Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • The Second Dimension
Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • The Second Dimension • Squares and polygons
Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • The Second Dimension • The Third Dimension
Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • The Second Dimension • The Third Dimension • Cubes and polyhedra
Classification • Dimensional Classification • The Zeroth Dimension • The First Dimension • The Second Dimension • The Third Dimension • The Fourth Dimension
Classification • Dimensional Classification • Classifying Figures
Classification • Dimensional Classification • Classifying Figures • “Dividing by 2”
Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • Points divide lines
Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • Points divide lines • Lines divide polygons
Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • Points divide lines • Lines divide polygons • Polygons divide polyhedra
Classification A cube is 3 dimensional because it can be split in two by a polygon.
Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • Points divide lines • Lines divide polygons • Polygons divide polyhedra • Ultimately helps classify shapes
Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • The Euler Characteristic
Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • The Euler Characteristic • The Greek letter χ (chi)
Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • The Euler Characteristic • The Greek letter χ (chi) • χ=f+p-e
Classification • Dimensional Classification • Classifying Figures • “Dividing by 2” • The Euler Characteristic • The Greek letter χ (chi) • χ=f+p-e • Our conclusions:
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.
Classification • Why is classification important? • Narrows which shapes are possibilities
Classification • Why is classification important? • Narrows which shapes are possible
Conclusion • Goal
Conclusion • Goal • Classification
Conclusion • Goal • Classification • The Euler Charactersitic
Conclusion • Goal • Classification • The Euler Characteristic • What comes next?