What Do You Know About The Mathematics Of Paper Folding?

1) In Kawasaki theorem, what is the sum of all odd angles?

90 degrees

180 degrees

270 degrees

360 degrees

The Kawasaki theorem states that in a triangle, the sum of the odd angles (angles opposite odd sides) is equal to 180 degrees. This means that if we add up all the odd angles in a triangle, the total will always be 180 degrees.

Explanation

The Kawasaki theorem states that in a triangle, the sum of the odd angles (angles opposite odd sides) is equal to 180 degrees. This means that if we add up all the odd angles in a triangle, the total will always be 180 degrees.

2) Can a sheet penetrate a fold?

No

Yes

Only when it is evenly divided

Only when folded into a triangular shape

A sheet cannot penetrate a fold because by definition, a fold involves bending or creasing a material, which creates layers that are stacked on top of each other. Therefore, there is no space for the sheet to pass through the fold.

Explanation

A sheet cannot penetrate a fold because by definition, a fold involves bending or creasing a material, which creates layers that are stacked on top of each other. Therefore, there is no space for the sheet to pass through the fold.

3) What is paper folding aso called?

Organics

Origami

Orifices

Origins

Origami is the correct answer because it is a traditional Japanese art of paper folding. It involves creating intricate and delicate designs by folding paper without the use of scissors or glue. The word "Origami" comes from the Japanese words "ori" meaning folding and "kami" meaning paper. This art form is not only visually appealing but also requires precision and patience. It is widely practiced and admired worldwide for its creativity and beauty.

Explanation

Origami is the correct answer because it is a traditional Japanese art of paper folding. It involves creating intricate and delicate designs by folding paper without the use of scissors or glue. The word "Origami" comes from the Japanese words "ori" meaning folding and "kami" meaning paper. This art form is not only visually appealing but also requires precision and patience. It is widely practiced and admired worldwide for its creativity and beauty.

4) Which set of equation do we use the paper fold for?

Integral equation

Mathematical equation

Research analysis

Infinitesimal equation

The paper fold method is commonly used to solve mathematical equations. By folding a piece of paper and using geometric constructions, it becomes possible to find the solution to certain types of equations. This technique is particularly useful for solving quadratic equations, as it allows for a visual representation of the problem and helps in understanding the roots of the equation. Therefore, the correct answer is Mathematical equation.

Explanation

The paper fold method is commonly used to solve mathematical equations. By folding a piece of paper and using geometric constructions, it becomes possible to find the solution to certain types of equations. This technique is particularly useful for solving quadratic equations, as it allows for a visual representation of the problem and helps in understanding the roots of the equation. Therefore, the correct answer is Mathematical equation.

5) Which of these is one of the rules used for producing flat-foldable patterns?

Makeriwk's theorem

Kovacic's theorem

Maekawa's theorem

Silva's theorem

Maekawa's theorem is one of the rules used for producing flat-foldable patterns. This theorem states that for a flat-foldable pattern, the sum of the number of edges, number of vertices, and number of faces minus the number of holes must equal 2. This theorem helps in determining whether a pattern can be folded flat without any overlaps or self-intersections.

Explanation

Maekawa's theorem is one of the rules used for producing flat-foldable patterns. This theorem states that for a flat-foldable pattern, the sum of the number of edges, number of vertices, and number of faces minus the number of holes must equal 2. This theorem helps in determining whether a pattern can be folded flat without any overlaps or self-intersections.

6) Which of the following shows the construction of paper folding models?

Multiple pattern

Single pattern

Mid-level surface

Crease pattern

The correct answer is "Crease pattern." A crease pattern is a diagram that shows the folding lines and creases required to construct a paper folding model. It is a visual representation of the steps needed to create the model, indicating where to fold and where to make creases. It serves as a guide for accurately folding the paper and achieving the desired shape or design.

Explanation

The correct answer is "Crease pattern." A crease pattern is a diagram that shows the folding lines and creases required to construct a paper folding model. It is a visual representation of the steps needed to create the model, indicating where to fold and where to make creases. It serves as a guide for accurately folding the paper and achieving the desired shape or design.

7) How do we identify map folding problems?

When creases are in straight form

When there are single patterns

When the different shapes are formed

When creases are orthogonal

When creases are orthogonal, it means that they are at right angles to each other. In the context of map folding, this can be used as a way to identify folding problems. When creases are not orthogonal, it can indicate that the folding is incorrect or that the map is not folded properly. Orthogonal creases are important for creating neat and organized folds, ensuring that the map can be easily unfolded and read without any confusion or distortion.

Explanation

When creases are orthogonal, it means that they are at right angles to each other. In the context of map folding, this can be used as a way to identify folding problems. When creases are not orthogonal, it can indicate that the folding is incorrect or that the map is not folded properly. Orthogonal creases are important for creating neat and organized folds, ensuring that the map can be easily unfolded and read without any confusion or distortion.

8) How many mathematical rules do we follow to produce flat-foldable patterns?

2

3

4

5

To produce flat-foldable patterns, we follow three mathematical rules. These rules ensure that the pattern can be folded without any overlaps or gaps. By following these rules, we can create a flat-foldable pattern that can be easily folded into a three-dimensional shape.

Explanation

To produce flat-foldable patterns, we follow three mathematical rules. These rules ensure that the pattern can be folded without any overlaps or gaps. By following these rules, we can create a flat-foldable pattern that can be easily folded into a three-dimensional shape.

9) Which of the following scientists did NOT work on this model?

Beloch Margharita

Humiaki Huzita

Jacques Justin

Justine Joaquin

The question asks which scientist did NOT work on the model. The names provided are Beloch Margharita, Humiaki Huzita, Jacques Justin, and Justine Joaquin. Out of these names, Justine Joaquin is the only one who did NOT work on the model.

Explanation

The question asks which scientist did NOT work on the model. The names provided are Beloch Margharita, Humiaki Huzita, Jacques Justin, and Justine Joaquin. Out of these names, Justine Joaquin is the only one who did NOT work on the model.