What Do You Know About Maekawa's Theorem?
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In mathematics, Maekawa's theorem is a theorem used in the mathematics of paper folding. It basically involves flat-foldable origami crease patterns that are determined by a variation of valley-creases and mountain-creases. Maekawa's theorem states that the numbers of mountain folds and valleys always differ by two at every vertex—no matter the direction.
- 1.Which aspect of mathematics is Maekawa theorem relevant.
- A.
Mathematics of setting cubes
- B.
Mathematics of folding paper
- C.
Mathematics of wave movement
- D.
Mathematics of scalar surfaces
- 2.What does Maekawa's theorem propose that the total number of folds at each vertex must be?
- A.
An odd number
- B.
A decimal number
- C.
An even number
- D.
Half of the angle
- 3.Who discovered this theorem before Maekawa worked on it?
- A.
S. Murata
- B.
B. Jurtala
- C.
Jan Nelson
- D.
Robert Oneil
- 4.What is one major flaw of this theorem?
- A.
It does not completely characterize the flat-foldable vertices
- B.
It shows only the angles of the vertical cortex
- C.
It is only applicable to folds greater than 180 degrees
- D.
The theorem is mutually exclusive to angles of a straight shape
- 5.When utilizing Maekawa's theorem, which one of the following is applicable at every vertex?
- A.
The number of mountain folds is the same in either direction
- B.
The number of valley and mountain folds is always the same in either direction
- C.
The numbers of valley and mountain folds always differ by two in either direction
- D.
The number of valley fold is the same in both directions of the vertex
- 6.Which of the following is applicable when using Maekawa's theorem for a flat-foldable crease pattern?
- A.
It is not possible to color the regions of the creases
- B.
It is always possible to color the regions between the creases with two colors, such that each crease separates regions of differing colors
- C.
Each crease seperates the regions into 5 different colours
- D.
It is not possible to color the region creases with two colors but each crease can still be separated to regions of differing colors
- 7.Which of these theorems is related to Maekawa's theorem?
- A.
Origami Theorem
- B.
Kawasaki Theorem
- C.
Murata Theorem
- D.
Vannelson Theorem
- 8.Which of these scientists used the theorem with the same results in the same year it was discovered?
- A.
Jacques Justin
- B.
Hull Thomas
- C.
Takahama Inoshi
- D.
Craig Edwards
- 9.In which mathematical publication was Maekawa's theorem first proposed?
- A.
Theorem of Wide Angles
- B.
Viva Origami
- C.
Theories of Origami Design
- D.
Mathematical Modeling Based on Origami Design
- 10.Which mathematical problem prompted Jun Maekawa to design the Maekawa's theorem?
- A.
Angle wideness of origami models
- B.
Crease regions in origami models
- C.
Fold number in origami models
- D.
Flat-foldability of origami models
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