What is the main challenge when trying to comb the hair on a ball in three dimensions?
The Hairy Ball Theorem

Interactive Video
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Mathematics
•
9th - 10th Grade
•
Hard
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5 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
The hair can be easily combed flat.
The hair can be combed flat only in two dimensions.
The hair can be combed flat if the ball is a doughnut.
The hair will always have a point where it sticks up.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the Hairy Ball Theorem mathematically prove?
A sphere can be combed flat without any issues.
A doughnut shape can have a vector field with no zero points.
A continuous vector field on a sphere must have at least one zero point.
A sphere can have a vector field with no zero points.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How does the Hairy Ball Theorem relate to wind patterns on Earth?
It suggests that wind can blow continuously without stopping.
It guarantees that there is always at least one point on Earth where the wind is not blowing.
It implies that wind patterns are unpredictable.
It states that wind can only blow in one direction.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a humorous way to challenge a mathematician according to the video?
Ask them to prove the Hairy Ball Theorem wrong.
Ask them to explain algebraic topology.
Ask them to comb a hairy banana.
Ask them to solve a complex equation.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a key condition for the Hairy Ball Theorem to hold true?
The object must be a perfect sphere.
The object can be smoothly deformed into a sphere without cutting or sewing.
The object must be a doughnut shape.
The object must be in two dimensions.
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