What Do You Know About Maekawa's Theorem?

10 Questions | Total Attempts: 104

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What Do You Know About Maekawa

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.


Questions and Answers
  • 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