& OTHER QUESTIONS: EQUAL A COFFEE MUG? WHAT IS TOPOLOGY? - - PowerPoint PPT Presentation

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Jun 17, 2023 235 likes •542 views

WHY DOES A DONUT & OTHER QUESTIONS: EQUAL A COFFEE MUG? WHAT IS TOPOLOGY? SARAH BLACKWELL WHAT IS TOPOLOGY? WHAT DOES IT MEAN FOR TWO THINGS TO BE THE SAME? 1 = 7 (mod 6) color versus colour congruent or similar triangles

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WHY DOES A DONUT EQUAL A COFFEE MUG? & OTHER QUESTIONS:

WHAT IS TOPOLOGY?

SARAH BLACKWELL

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WHAT IS TOPOLOGY?

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WHAT DOES IT MEAN FOR TWO THINGS TO BE THE SAME?

“color” versus “colour” 1 = 7 (mod 6) congruent or similar triangles

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TOPOLOGY IS A WORLD WITH ITS OWN NOTION OF SAMENESS.

“topologically equivalent” studying shapes and spaces

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TOPOLOGICALLY EQUIVALENT

Sphere = soccer ball (hollow on the inside) ALLOWED: bending, stretching NOT ALLOWED: poking holes, cutting, taping

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TOPOLOGICALLY EQUIVALENT

By User:LucasVB - Own work, Public Domain, https://commons.wikimedia.org/w/index.php?curid=1236079

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TOPOLOGICALLY EQUIVALENT

Torus = inner tube or surface of a donut (hollow on the inside)

= ?

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TOPOLOGICALLY EQUIVALENT

Torus = inner tube or surface of a donut (hollow on the inside)

=

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GAME TIME!

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X

GAME TIME!

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O X

GAME TIME!

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X O X

GAME TIME!

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X O X O

GAME TIME!

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X O X X O

GAME TIME!

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X O X X O O

GAME TIME!

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X O X X O X O

GAME TIME!

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X X X

GAME TIME!

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X X X

GAME TIME!

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X X X

GAME TIME!

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X X X

GAME TIME!

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X X X

GAME TIME!

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X X X

GAME TIME!

X

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X X

GAME TIME!

X

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X X X

GAME TIME!

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GAME TIME!

X X X X X X X X X X X X

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WHAT’S THE NAME OF THE GAME?

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TORUS TIC TAC TOE

Why?

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TORUS TIC TAC TOE

Why?

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PICTURE REFERENCES

Slide #4
https://ncatlab.org/nlab/show/Introduction+to+Topology
Slide #6
https://www.cems.riken.jp/en/laboratory/qmtrt
Slide #30
https://www.amazon.com/Shape-Space-Chapman-Applied-

Mathematics/dp/0824707095

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THANKS FOR LISTENING!

QUESTIONS?

If you want to learn more about topology, this book is a great place to start