What Do You Know About The Carpenter's Problem?
In the carpenter's problem, you are to provide answers on the likelihood of a simple polygon being moved to a point where all vertices are convex when the length of the edges is properly established. The problem became popular following attempts by mathematicians to solve it in the 21st century. How conversant are you with geometry problems? Do not be found wanting!
- 1.
Who was credited to formulate a combinatorial proof in the terminology of robot arm motion planning?
- A.
Ileana Strianu
- B.
John Pardon
- C.
Henry Euler
- D.
Jude Pythagoras
Correct Answer
A. Ileana Strianu -
- 2.
In which year did Strianu and Whiteley provide an application for the problem?
- A.
2013
- B.
2014
- C.
2015
- D.
2017
Correct Answer
C. 2015Explanation
Strianu and Whiteley provided an application for the problem in the year 2015.Rate this question:
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- 3.
Which part of the shape is most concerned in the solution by Strianu and Whiteley?
- A.
Edges
- B.
Vertex
- C.
Segment
- D.
Angle
Correct Answer
B. VertexExplanation
The solution by Strianu and Whiteley is most concerned with the vertex of the shape. This means that they focus on the point where two or more edges of the shape meet. They likely analyze the properties and characteristics of the vertex to find a solution to the problem at hand.Rate this question:
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- 4.
In this problem, what change has an effect on the Jordan curve?
- A.
It is made concave
- B.
It is made convex
- C.
It is curved
- D.
It is straightened
Correct Answer
B. It is made convexExplanation
When the Jordan curve is made convex, it means that the curve is bent outward, creating a shape that does not intersect itself. This change in curvature affects the overall shape of the curve, making it more open and allowing for a larger area to be enclosed by the curve.Rate this question:
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- 5.
Who is popularly known to generalize carpenter's problem?
- A.
John Chase
- B.
Isaac Newton
- C.
Alexander Fleming
- D.
John Pardon
Correct Answer
D. John PardonExplanation
John Pardon is popularly known to generalize carpenter's problem.Rate this question:
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- 6.
Which year saw the content generalization of this problem?
- A.
2010
- B.
2009
- C.
2002
- D.
2007
Correct Answer
B. 2009Explanation
The content generalization of this problem occurred in the year 2009.Rate this question:
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- 7.
Which is the term for the continuous transformation of a closed curve in the plane and eventually convexifying it?
- A.
Curve shortening flow
- B.
Flow convexing
- C.
Convexing
- D.
Concave flow
Correct Answer
A. Curve shortening flowExplanation
Curve shortening flow refers to the continuous transformation of a closed curve in the plane, where the curve is gradually shortened and eventually becomes convex. This process involves the curve evolving over time by shrinking and smoothing out any concave regions, resulting in a convex shape. Therefore, curve shortening flow is the appropriate term for this phenomenon.Rate this question:
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- 8.
How many sides should be observable in an ideal trapezium?
- A.
3 sides
- B.
10 sides
- C.
8 sides
- D.
6 sides
Correct Answer
D. 6 sidesExplanation
An ideal trapezium should have 6 sides. A trapezium is a quadrilateral with one pair of parallel sides. The other two sides are non-parallel and can have any length. So, in an ideal trapezium, there are 4 sides that form the quadrilateral shape, and 2 additional sides that are parallel to each other. Therefore, a total of 6 sides should be observable in an ideal trapezium.Rate this question:
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- 9.
Which year saw the permanent solution to carpenter's problem provided by Italian mathematicians?
- A.
2013
- B.
2012
- C.
2007
- D.
2003
Correct Answer
D. 2003Explanation
In 2003, Italian mathematicians provided a permanent solution to carpenter's problem.Rate this question:
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- 10.
Which of these mathematicians was not involved in providing a solution to the problem in 2003?
- A.
Dufresne
- B.
Domaine
- C.
Connelly
- D.
Rote
Correct Answer
A. DufresneExplanation
The question asks which mathematician was not involved in providing a solution to the problem in 2003. The correct answer is Dufresne.Rate this question:
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