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Symmetrical Origami

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Symmetrical Origami

Taylor Rumsey

- How can we use origami to model different types of symmetry?

- Students will learn the 3 different types of symmetry (Reflection, Rotation and Translation), and then demonstrate their knowledge by creating a “Symmetrical Origami Art Project”
- Students will become familiar with Origami as a Japanese art form; and they will master some of the folding techniques (turning a rectangular paper into a square paper without a ruler, and making sure a fold is lined up perfectly)used in this Japanese form of art, which will also be demonstrated in their Origami art project
- Students will use the 4 explicitly taught Origami folds (kite, skinny kite, triangular 1 and triangular 2) to create an artwork that reflects the different types of symmetry (more specifically reflection and rotation symmetry)

- Symmetry- when one shape becomes exactly like another if you flip it around, slide it, or turn it.
- Reflection Symmetry —when you fold a 2-D figure in half, the two parts will match up perfectly; also known as mirror symmetry
- Rotation Symmetry- the image/figure can be turned a certain amount and look exactly the same; also known as radial symmetry
- Translation Symmetry- moving an object to the right, left, up, down or diagonally
- Line of symmetry-divides a figure into two equal halves (can be horizontal, vertical or diagonal)

Origami-the Japanese art of folding paper into decorative shapes and figures

Fold-to bend something over on itself so that one part of it covers another

Kite Fold- a fold that looks like a kite

Skinny Kite Fold- a fold that looks like a skinny kite

Triangular Fold- a fold that looks like a triangle

Example:

- Also known as “Mirror Symmetry”
- When you fold a 2-D figure in half and the two parts will match up perfectly

Non-example:

- Divides a figure into two equal halves (can be horizontal, vertical or diagonal)
- A shape can have more than one line of symmetry

How many lines of symmetry? Where are they?

- Also known as “Radial symmetry”
- The image can be turned/rotated a certain degree and look exactly the same as it originally did

Which shape is not an example of rotation symmetry?

Correct:

- Moving an object to the right, left, up, down or diagonally
- Your initial shape does not move
- The translated shape is the one that is moved
- The translated figure may not be rotated or flipped!

Incorrect:

Which option shows translation symmetry?

- Origami- The Japanese art of folding paper into decorative shapes and figures
- The word “Origami” comes from the Japanese words oru (to fold) and kami (paper)
- Paper folding in ancient Japan was used only for religious purposes
- Early 1600’s-paper folding became a recreational activity as well
- Late 1700’s- first written instructions for paper folding appeared
- Origami was/is a huge part of Japanese culture
- It is now an art form used all over the world!

Examples

2. Skinny Kite Fold

- Kite Fold

4. Triangle Fold #2

3. Triangle Fold

Step 2: Take outside corners and line them up with the crease that you made in the middle

Step 1: Fold the square paper in half to make a triangle

The Skinny Kite Fold

Step 2: Take outside edges and fold them towards the center once more

Step 1: Make regular Kite fold

Triangular Fold 1

Step 3: Open fold once; Take the bottom corners and line the edges up with the fold line you created

Step 1: Fold Square in half (hotdog style)

Step 2: Fold paper in half again to create a small square

Triangular Fold 2

Step 1: Fold the square in half diagonally to make a large triangle. Open it, and fold it the opposite way. Open again.

Step 2: Push two opposite triangles together and pinch the top

Step 3: Squish flat!

You will create a symmetrical design using the origami folds you make!