What Do You Know About The Carpenter's Problem?

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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

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

C. 2015
Explanation
Strianu and Whiteley provided an application for the problem in the year 2015.

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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

B. Vertex
Explanation
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.

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• 4.

In this problem, what change has an effect on the Jordan curve?

• A.

• B.

• C.

It is curved

• D.

It is straightened

Explanation
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.

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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

D. John Pardon
Explanation
John Pardon is popularly known to generalize carpenter's problem.

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• 6.

Which year saw the content generalization of this problem?

• A.

2010

• B.

2009

• C.

2002

• D.

2007

B. 2009
Explanation
The content generalization of this problem occurred in the year 2009.

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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

A. Curve shortening flow
Explanation
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.

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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

D. 6 sides
Explanation
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.

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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

D. 2003
Explanation
In 2003, Italian mathematicians provided a permanent solution to carpenter's problem.

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• 10.

• A.

Dufresne

• B.

Domaine

• C.

Connelly

• D.

Rote