Origami Folding Techniques

Origami Folding and Flat-Folding

• A flat-folded origami model must satisfy the alternating sequence of mountain and valley folds at each vertex.
• The number of mountain folds and valley folds meeting at a vertex must satisfy a certain condition for the model to fold flat.
• For a vertex to result in a flat-fold, it requires an alternating sequence of mountain and valley creases.
• A vertex with an odd number of mountain or valley folds cannot produce a flat-fold.
• A vertex with an equal number of mountain and valley folds can potentially lead to a flat fold.

Vertex Analysis in Origami

• In this example, Darryl observed 5 mountain folds and 3 valley folds at a particular vertex.
• The number of mountain folds (5) and valley folds (3) at the vertex is not equal.
• The difference in the numbers of mountain and valley folds at the vertex is 2.

Flat-Folding Condition Violation

• The observed vertex configuration (5 mountain folds, 3 valley folds) violates a crucial rule for flat-folding origami models.
• A vertex in a flat-folded model must have the same number of mountain and valley folds, or a difference of 2.
• The difference must be a positive or negative number that's a multiple of 2, which is required for a vertex to flat fold. In the provided example, the difference is 2 and thus doesn't violate this requirement.
• Since the difference between mountain and valley folds at the vertex is not a multiple of two, the origami will not fold flat.

Explore the principles of flat-folding origami models through vertex analysis. Understand the significance of mountain and valley folds and the conditions required for a model to fold flat. Delve into examples showcasing how different configurations affect the folding process.