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Knot Theory

Test your knowledge of Knot Theory, a branch of mathematics that studies knots, which are closed curves in 3-dimensional space.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

What is the simplest knot?

  1. Unknot
  2. Torus Knot
  3. Trefoil Knot
  4. Figure-Eight Knot
Question 2 Multiple Choice (Single Answer)

What is the name of the knot that is formed by tying a simple overhand knot?

  1. Unknot
  2. Torus Knot
  3. Trefoil Knot
  4. Figure-Eight Knot
Question 3 Multiple Choice (Single Answer)

Which of the following is a knot invariant?

  1. Knot type
  2. Crossing number
  3. Genus
  4. Unknotting number
Question 4 Multiple Choice (Single Answer)

What is the crossing number of a knot?

  1. The number of times the knot crosses itself
  2. The number of components in the knot
  3. The genus of the knot
  4. The unknotting number of the knot
Question 5 Multiple Choice (Single Answer)

What is the genus of a knot?

  1. The number of times the knot crosses itself
  2. The number of components in the knot
  3. The number of holes in the knot's complement
  4. The unknotting number of the knot
Question 6 Multiple Choice (Single Answer)

What is the unknotting number of a knot?

  1. The number of times the knot crosses itself
  2. The number of components in the knot
  3. The genus of the knot
  4. The minimum number of crossing changes required to unknot the knot
Question 7 Multiple Choice (Single Answer)

What is the Alexander polynomial of a knot?

  1. A polynomial that is associated with a knot
  2. A knot invariant
  3. A knot type
  4. A crossing number
Question 8 Multiple Choice (Single Answer)

What is the Jones polynomial of a knot?

  1. A polynomial that is associated with a knot
  2. A knot invariant
  3. A knot type
  4. A crossing number
Question 9 Multiple Choice (Single Answer)

What is the HOMFLY polynomial of a knot?

  1. A polynomial that is associated with a knot
  2. A knot invariant
  3. A knot type
  4. A crossing number
Question 10 Multiple Choice (Single Answer)

What is the Kauffman bracket of a knot?

  1. A polynomial that is associated with a knot
  2. A knot invariant
  3. A knot type
  4. A crossing number
Question 11 Multiple Choice (Single Answer)

What is the Conway knot?

  1. A knot that is named after John Horton Conway
  2. A knot that is formed by tying a simple overhand knot
  3. A knot that has a crossing number of 11
  4. A knot that has a genus of 2
Question 12 Multiple Choice (Single Answer)

What is the Gordian knot?

  1. A knot that is said to have been tied by King Gordius
  2. A knot that is impossible to untie
  3. A knot that has a crossing number of 13
  4. A knot that has a genus of 3
Question 13 Multiple Choice (Single Answer)

What is the trefoil knot?

  1. A knot that is formed by tying a simple overhand knot
  2. A knot that has a crossing number of 3
  3. A knot that has a genus of 1
  4. All of the above
Question 14 Multiple Choice (Single Answer)

What is the figure-eight knot?

  1. A knot that is formed by tying a figure-eight knot
  2. A knot that has a crossing number of 4
  3. A knot that has a genus of 1
  4. All of the above
Question 15 Multiple Choice (Single Answer)

What is the Whitehead link?

  1. A link that is formed by linking two unknots
  2. A link that has a linking number of 0
  3. A link that has a genus of 1
  4. All of the above
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